I did this trip 3 years ago. We went to 3 different countries, 5 different cities. It was tiring for a 3 week vacation, but totally enjoyed it. Our itinerary looked like this

Flew into Bangkok, Thailand then transfered to Vientiane, Laos for 4 days
Flew to Luang Prabang, Laos for 3 days
flew to Phuket, Thailand for 4 days
flew to Singapore for 6 days
flew to Bangkok Thailand for a few more days before heading home

Each location is just amazing. But there's a whole lot more places in SE Asia you can visit. There's Cambodia, Malaysia, Indonesia. Flying around is easy too. Lots of discount airlines costing around USD100 for each flight.