Some good suggestions, don't try to do 3 or more solely beach vacation spots. Thailand is, of course, my favorite, though Phuket can be very rainy in May and June. Not all day long, but you might not be into doing massages while you wait for the rain to pass. OK, so that was a little sarcasm. Bali would be better if you can push it to late June or July, the best season there. This past May was great in Vietnam and the beaches are great, as well as a very well priced location with plenty of other things to do. My friends just did Vietnam in May and they loved the city scene in Saigon and Hanoi, the beaches of Nha Trang and Da Nang, and they did the 3 day/2 nt boat cruise in Ha Long Bay which they felt was the high point. If you are set on a RTW, try first heading to Europe (I'm springing for my younger son's honeymoon in Aug to Italy for 13 days, and it was easy on SPG points, though the 2 Business class awards on AA came to 540k total. Ouch.) The beaches are also nice in certain places in the south of France, Antibes especially, which also has one of my favorite Picasso "museums," his previous residence of course.. And, plenty of other activites-museums in Nice, perfume factories in Grasse/Mougin, casinos in Monte Carlo, and if it's late May, try for tickets to the F1 race. Of course, outdoor restaurants everywhere. The whole area from Cannes to Monte Carlo can get expensive and difficult to use points during the later part on May between the Cannes Film Festival and F1 race, but I've done it a number of times. Just takes a little planning.
I've pieced together RTW trips, usually 3 tickets, sometimes including awards. Usually the RT is much cheaper than one way to DFW-NCE, and I've thrown away the return, though with some good planning, can set the table to a repeat trip some time later, doing te reverse RTW using the returns. Then NCE-BKK/HKT/SGN/HAN and then back to DFW. If the miles aren't going far enough, the fares from Europe to Asia can usually have some premium fare deals, even one way. I recently did OSL-LHR-HKG on CX PEone way for about $621 and the fares to BKK, HKT, SGN, HAN OR DPS aren't too much more. It's not as nice as CX J but then check some other carriers that you have miles on for one ways.
Enjoy