There are lots of high rise hotels. I stayed at the Fraser Suites Sukhumvit a couple of years ago and really liked it. I believe I was on the 29th floor. Fits your budget. OK location. The apartment I had was quite nicely appointed. View OK. I would guess that requesting a high floor shouldn't be a problem. Most people probably don't ask one way or the other.

Centara Grand at Central World fits your budget as well. I have not stayed there and it seems to get mixed reviews. Good location though. Open air restaurant on the 55th floor