Public bus is available from the intercity bus station to the city center.
Here is the link to help you.
http://www.gaziantep-bld.gov.tr/otobushareket/index.php?kalkissec=38

After visiting the castle you can walk to the Zeugma Museum which is close to the Archeological Museum.
(Arkeoloji Müzesi )
Address: İstasyon Caddesi No:2 ŞEHİTKAMİL/GAZİANTEP
Tel: (342) 324 88 09 Faks: (342) 324 38 22
http://www.gaziantepcity.info/tr/gaziantep_arkeoloji_muzesi.haritasi
ZEUGMA MUSEUM (ZEUGMA MOZAİK MÜZESİ)
Address:Mithatpaşa Mahallesi Hacı Sani Konukoğlu Bulvarı 27500, Şehitkamil

From the museum you can take a bus to the main intercity bus station(otogar)

And this is the map of Gaziantep showing the castle.

http://www.gaziantepcity.info/tr/gaziantep_kalesi.haritasi

Thanks, is this the Zeugma museum? Gaziantep Zeugma Kongre Küültür Ve Müze Merkez? I got this one google maps, it seems to be pretty far away from fort(2 kms), how much would a taxi cost for this distance?

And are there any good eateries around the Mosaic museum? Or are they most centred around the fort and old city?

A taxi wouldn't cost much. 5-6 TL(2-3 €)
Admission fee is 8 TL (3,5 €)
The museum is closed on Mondays and visiting hours are:
April-Oct.(9.00-17.00) and Nov.-March.(9.00-17.30)
and this is the link
http://www.muze.gov.tr/gaziantep-en

Most of the restaurants are around the fort and Gaziantep is famous with its special cuisine however most are not suitable for a vegetarian.

Eat your breakfast at any place that serves "Katmer"
The most famous is Orkide Pastahanesi, but it is about two kilometres from the fort.

- Baklava is sold everywhere, however there are major differences in taste. Imam Cagdas, Kocak and Gulluoglu are the most popular. I am sure that there may be some cheaper baklava but it will not be worth your while to buy it there and carry it around with you if you will be back in Istanbul eventually.

Currently prices for good baklava with lots of green pistachios range from 40 to 50TL/kilo. You can get decent baklava which is shipped to istanbul and sold here for the same price at places like Baklava Diyari in Sirkeci and Koskeroglu in Karakoy.

You do not need to ask for "local" places, because everything will be local there.

Unfortunately, it will not be easy for you to find vegetarian dishes in Southeastern Turkey.

No matter how used you may be to spicy hot food, be careful with the green peppers in Urfa.

Thanks senozkadir and otherchelebi, I would be going to Sanliurfa after Antep, and then to IStanbul, but I wont be in Istanbul for long,maybe a couple of hours. So I guess I should buy from Gaziantep itself.
What would you suggest ordering in Gaziantep,since I believe not many people would know english, it's beter to have a few names of dishes ready. KAtmer looks like a sweet dish,right?
Do they have salads,peynir lahmacun and all?

And if I had to take a quick walk through the market,where should I go?

You may order chickpea wrap(nohut dürüm) or aubergine wrap(patlıcan dürüm) at Fiko'nun Yeri
Address : Alleben Mah. Şair Nabi Sok. No:13/C Gaziantep

The link below (although in Turkish) will give you an idea about the city.(see photos)

http://kitchensweetkitchen.blogspot.com/search/label/Gaziantep

the map of Fiko'nun Yeri

http://www.mekanist.net/gaziantep/restoran/fikonun-yeri

IMO Coppersmiths Bazaar(Bakırcılar Çarşısı) and Spice Bazaar(Baharatçılar Çarşısı) are the highlights.

Thanks, that is some brilliant advice!!

We enjoyed walking around Zincirli Bedesten, near the coppersmiths and back. The old city market streets are not so extensive.

Gaziantep lahmacun uses garlic and Urfa lahmacun has an onion base. It may be possible for you to order lahmacun without meat.

"ETSIZ LAHMACUN, LUTFEN"

Please read my reviews on various places in Gaziantep and for Rum Kale on Trip Adviser.

Katmer is very thin pistachio and water buffalo cream dessert, freshly prepared and served hot. We prefer it to baklava, but it does not travel.

On that note, if you get the dry baklava (without any syrup) it will travel best. You can eat it comfortably for possibly two or three weeks after you get home, and longer if you keep it in the fridge. Called KURU BAKLAVA.

Thanks, can you suggest any place to try katmer,close to the fort?
I would be going to Halfeti,but from Sanliurfa. Does the boat(from halfeti) go anywhere close to this point: http://www.belgeci.com/UserFiles/rumkale06022007005.JPG ?
Or is this place accessible only from the Gaziantep route?

I am sure you will find katmer at most places which serve breakfast and also which sell baklava.

The route to that spot requires walking up the hill from the small boat landing reached either by land transport from Gaziantep or Adiyaman or by boat from Halfeti.
However, if you are on a tour the boat from halfeti may not wait while you land and climb up to take this photo, unless it is a private hire.

I would be taking a boat from halfeti. What should I tell the boatman? And how much would a small private boat cost? Is the climb a short one?

Last year (did you read my review?) we paid TL200, but it could have been less, 150 or 180. However, it is a long cruise and petrol is very expensive.

Your guess is as good as mine for the climb, from looking at the photo at the link you gave.

Do you get the opportunity to disembark at Rumkale and climb up to the ruins? And is there much to see there?

I was just think of changing plan a little bit, I was initially planning to do Antep-Kahta-Urfa,day trip to Rum kale.
Do you think this is feasible: Antep-Kahta-Yavuzeli-Sanliurfa? Are there buses between Adiyaman and Yavuzeli and between Yavuzeli and Halfeti?

Croesus , it was too cold the day we made the trip and we were not prepared to climb up. Please read my Trip Adviser review of Rum kale.

ash, I doubt that you can get buses between Yavuzeli and Halfeti. However, you may get to Kadaba village from Yavuzeli for Rum Kale. That is only 25 kilometres.

So will I get a boat for Rum kale and halfeti from kadaba, and accommodation too? Doesn't sound very hassle free.

Sorry for the misprint. It should be Kasaba village.

Ash, I am sorry that I could not persuade you to read my review.

If you look at the map, you will see that Kasaba is only hundred meters or so cross from Rum kale and is near the vantage point your photograph was taken. There are cheaper boats from a pier at that location, to cruise around the fortress and possibly let you climb up to Rum Kale. Whereas Halfeti is many kilometers to the Southeast.

If you get to Yavuzeli and then Kasaba, you do not need to go to Halfeti or Urfa to visit Rum Kale. Just stay at Yavuzeli or get back to Gaziantep.

Oh..I have read your review, however I have to cover Sanliurfa and my flight back to Istanbul is from Urfa itself. And I have 3 days in SE Turkey, I leave on the 4th day in the morning.
So if I go to Rum kale from Yavuzeli, I still have to go Sanliurfa. I'm trying to find out if Gaziantep-Kahta-Yavuzeli-Sanliurfa is better than gaziantep-Kahta-Sanliurfa and Halfeti day trip.
IS there accommodation in Yavuzeli?

I mean kasaba village..

I think you'll find the nearest hotels are in Halfeti, Birecik or Gaziantep. Although there might possibly be somewhere to stay in Yavuzeli, but almost certainly not in the tiny village of Kasaba.

I don't think I'll be visiting Rumkale yet (it's not even on my to-do list) maybe in a few years time when they've tidied it up a lot more - "stone houses will be transformed into boutique hotels" - http://www.hurriyetdailynews.com/rumkale-preparing-to-welcome-tourists.aspx?pageID=238&nid=25259

That's good news..infact there is a boutique hotel already in Halfeti, Halfeti Socrates Antik Konukevleri.