Does a sub need to be on the floor?

Hsu subs can be had for not a lot of money and give pretty good performance for the buck.
Using spikes with subs should also help decouple them.
Wolfer- a good sub, properly tuned for music shouldn't be 'boomy'.

Regarding cost, you can find a used REL for a couple hundred bucks (I recently added a REL Q108II to my Q150e and it sounds great…8" woofer, lots of adjustability)…good subs "charge" a room regardless of the music’s low frequency content rendering everything more lifelike, which is a good thing if that’s what you want to hear. Also note that a well designed musical sub allows you to "tune" your room by moving the sub around and adjusting the output, and once you get it right where you want it you can’t imagine not having that benefit as it seems to open everything up. Very few main speakers can get close to actual bass so using a sub is an easy path to accurate sound. Plus, you can get drunk and dance around like an idiot.

You simply it hang it on the wall to save floor space :-)

The ceiling…stick it to the ceiling.