skip the car rental--if you need to access otehr towns, bus is best, then train for most side trips
City is fairly compact and transport is cheap--city trams and buses are fun, too!
Haven't used the subway but they say it's pretty manageable. Lots of young people speak English if you need help.
Popular tourist areas are walking tours, due to traffic/cobbled no-car streets.
Apts--I can recommend one bldg/owner (below castle steps) www.roomsinprague.com tell Josef you're Delta
www.thunovska19.com never stayed but the apts I saw are quite nice--ask for Delta $
luxurylink.com has a fabulous deal for upscale Hotel Hoffmeister (also near castle steps)
they ahve offers for some other hotels as well--all top shelf joints!!
Some people prefer Old Town--I don't but take a look at apartments-in-prague.org for bets areas--Mala Strana, Old Town are best chocies to access most sights
You can get so-so price on Hiltons thru resx.com (deltanet)--no charm like apts tho!

I go often when Boss does the PRG rotations so fee free to ask more. When are you going?