Good day, I belive you have a good budget for a nice accomodation, Doha is a very small city so dont worry about driving at all, as for the serviced appartment you can check EZDAN Towers ( West Bay) or Les Roses ( Banks street) you can also go to a compound I would highly suggest Beverly hills compound Rayan ( I used to live there) apartments are not serviced but the compound is very well maintained, great pool combined with a nice loungy clubhouse, squash court, a very useful gymn and a very useful supermarket. Also AL Raeis offer laundry service overthere. You can also check for accomodtaion here on QL in the classified section. Good luck