I have been in Jasper 4 or 5 times in the past 11 years.
(Twice with my wife). I/we stay in the HI Hostel about 4 miles out of Jasper near the north end of the Icefield Highway.
http://www.hihostels.ca/westerncanada/1478/HI-Jasper.hostel
It has been decades since I have been to Banff/Lake Louise.
I don't recall the scenery being any more majestic there than in Jasper. I/we arrive on the ViaRail Canadian. There are places to rent a car within walking distance of the train station and the Brewster tour bus counter is in the east half of the train station. To save some time you could fly to Edmonton and ride the Canadian from Edmonton to Jasper.

I would certainly hire a car.I dont know whether it's possible to fly in to Edmonton and out from Calgary.That would be the most efficient way.For Jasper I think three days will be ok.We stayed at the Becker chalets(great).The wonderful road to Banff will take one day.From Banff you can visit Lake Louise and in my opinion the greatest lake of all Lake Moraine and the neighbouring park Yoho.Paul

Hi,

Your timing is too early in the season for viewing wildflowers in the mountains. Prime blooming season is mid-July to mid-August. However, because it's early in the season there will be less people than July/August.

Also, depending on the winter/spring conditions, many of the hiking trails will be wet/muddy at the best and still snow-covered at worst. For the best hiking that time of year, you need to go to farther east into Kananaskis country where the trails are at lower elevations and the snow melts earlier.

We are RVers but when we travel to places like National Parks, we prefer to motel it. With an rv it takes time to set up/break down i.e. fill/empty gray/black tanks, driving is more difficult, and you're limited on where you can go. In my opinion, travelling by car through the mountains and just motelling it is so much easier.

With approximately 10 days, I might do it this way: fly into Calgary (if early, rent a car and head to Banff). Spend 2 nights in Banff, 1 night in Lake Louise, 1 night in Revelstoke (the drive from Lake Louise to Revelstoke is fantastic - lots to see), 1 night back in Lake Louise (sets you up for the Icefield Parkway next morning), 3 nights in Jasper, 1 night back in Banff (this gives you a chance to do the IP both ways). It also positions you well the next day to head back to Calgary. 1 night in Calgary. As for must-sees, there is so much that I would suggest reading up on travel forums like this one & Trip Advisor. You'll gain so much info on how/where to travel and what to see & do.

As some have mentiond it can be brisk in June. I think loveroadtripsmb itinerary is a good one by car.Lake Louise is nice but limited amount of hotels compared to Banff where you get a lot of choice at different price points. Either way , have a great trip. The A1( Bow valley parkway) is a great side route to take between Banff and Lake Louise and you can hike the Johnstone canyon there .
http://www.tripadvisor.ca/Attraction_Review-g154911-d1907318-Reviews-Bow_Valley_Parkway-Banff_Banff_National_Park_Alberta.html