Well, what is your budget?

The tourist infrastructure is more developed in Croatia, but if you had a lot of money, Sveti Stefani in Montenegro is certainly a gorgeous location and the towns along the Bay of Kotor are lovely. But you can do those on a day trip from Dubrovnik.

Most of the activities you want are available at many locations on the Croatian coast and islands. The question is what area most appeals to you. Istria is much like Tuscany, the area south of Split to Dubrovnik looks like the California coast. There are various national parks inland, Pitlive Lakes being the most famous. So it is hard to tell what to advise when there is so much variety.

I'll leave it to others to deal with cycling. I wouldn't even if I could because many of the very scenic roads are steep and narrow and the drivers are Mediterranean. That doesn't mean I wouldn't rent a bike locally or in Istria where things are more spread out.

It will be hot at that time in September. Treating yourselves well will mean making sure you have air conditioning! Food is generally outstanding, excellent beer, wine not quite as good as the local think in many cases. Beaches are generally shingle rather than sand. What else?

Croatia is a gorgeous country where they like American. Montenegro is a gorgeous country.

Ackislander is spot on.
September's can still be very warm in Croatia's coastline (and most of the countryside) but nights are more pleasent.
Far less people but not empty.

Rafts are on rivers Dobra, Korana (near Plitvice and attractive Rastoke site), Krka (National park) , Zrmanja (best canyons).

Plitvice lakes are worthy of one day trip. Preferably on a sunny day.

Dubrovnik is shame to miss if you're already in Croatia.
Game of Thrones were and are shot in Dubrovnik.

Best voted restaurants in Croatia in 2012.

1. Bistro Apetit, Zagreb
2. Takenoko, Zagreb
3.Prasac, Zagreb
4. Plavi Podrum, Volosko
5. Batelina, Banjole
6. Dubravkin put, Zagreb
7. Le Mandrać, Volosko
8. Draga di Lovrana, Lovran
9. Kukuriku, Kastav
10. Nautika, Dubrovnik
11. Apetit City, Zagreb
12. San Rocco, Brtonigla
13. Vinodol, Zagreb
14. Johnson, Mošćenićka Draga
15. Mano, Zagreb
16. Pelegrini, Šibenik
17. Baltazar, Zagreb
18. Foša, Zadar
19. Carpaccio, Zagreb
20. Damir & Ornella, Novigrad

Restoran prijatelj vina (Wine wise restaurants)

1.Dubravkin put, Zagreb

2. Plavi podrum, Volosko

3. Apetit City, Zagreb

Regionalne liste

(Regional list)

Slavonija i Podunavlje

1. Hotel Dunav, Ilok

2. Kormoran, Bilje

3. Klub restoran Waldinger, Osijek

Središnja Hrvatska

1. Mala Hiža, Mačkovec

2. Špiček, Zaprešić

3. Kod špilje, Otruševac

Istra i Kvarner

1. Plavi podrum, Volosko

2. Batelina, Banjole

3. Le Mandrać, Volosko

Dalmacija

1. Nautika, Dubrovnik

2. Pelegrini, Šibenik

3. Foša, Zadar


Zagreb can be vibrant and pleasent in that period.
Also you can do a bit of shopping there. Good road connection with Istria.

Istria is very romantic with excellent food and wellness.
Towns to visit:
Opatija (treshold of Istria, grand hotels and spa)

Rovinj (very romantic)

Pula (Roman Arena often in programme with world star musicians)

Motovun (biggest truffle site in Croatia - check Anthony
Burdoain's episode of Croatia)

Savudrija for luxury wellness
http://www.kempinski.com/en/istria/hotel-adriatic/welcome/