The poshest areas in Cheltenham are Tivoli and Charlton Kings at the moment. Montpellier would suit, and Landsdown is good. Leckhampton is nice, quiet, if you're at the Warden Hill side of Leckhampton it's only 10 minutes to the train station. (Shurdington Rd sort of splits these two areas). There are new houses and a new school on Shurd Rd now, it's quite sought after.
But it depends what you're after; cul de sac house, or more private? The Reddings is a nice area for families. Along Bath Road is a great location, a community of it's own.
Avoid: Springbank, Whaddon, Hester's Way, Rowanfield, basically West Cheltenham has more built up areas of social housing and is 'rougher' but as rough goes, it's not awful.
Cheltenham is a great town, the festivals (Literature, Jazz, Science etc) attract a lot of visitors and celebs, all the schools are decent (Pates and the Ladies College stand out). Lots of good pubs and restaurants. The shopping is very good.
Pop me a PM of any houses you're considering, if you like - Chelt is my hometown.