I think a few people have gone seriously off coarse here.....
Back to the original post.....
Mirdif is excellent value for money on the whole. Yes there is considerable noise from the aircraft, but seek accomodation on on the right side, and it is reduced significantly.
Bur Dubai is an Ok area, but again can be very noisy with all the traffic that move's around the busy streets. Staying closer to the Burjuman Shopping Centre side of Bur Dubai, will avoid some of the unsavory sights of the 'Old Spinney's'/Ramada Hotel side. (Locals to Dubai will know what I mean)
Sharjah is certainly cheaper than Dubai, however there are considerable changes in lifestyle to think about. Traffic from Sharjah to Dubai being one of the main one's. Other's could be how sociable you are as a person, and therefore the lask of places to go in Sharjah require's a drive/taxi to Dubai for a night out.
Jumeirah is the expat place, and is where anybody, who is anybody will tend to reside. It's close to the beach, and has plenty of amenities, and as a result is consierably more expensive than Mirdif.
Shk Zayed Road. The sight of high rise tower blocks will not appeal to those suffering with vertigo, but will provide some good views from the higher heights! The higher you go, so does your rent. All have good facilities, ie, swimming pools, gym's, sauna's, squash courts, and centrall AC, however the constant rumble at the lower levels of the eight lane highway which runs between them can be annoying, as with the constant building working.
Overall, plently of places to look at, to suit many budgets. If your budget can't stretch to some of the above, consider a place called "The Gardens", next to Jebel Ali Village. Large apartment complex, set out in pleasant surroundings, and very cost effective. It's just a trek back into town! 25mins town, 30-40mins airport depending on route.
What ever you do good luck,
AOG007