For your first time in Vegas, I would not recommend staying downtown.
Yes, you will pay less for your room and the Nugget is a very nice place, nothing wrong there. But downtown definately does not have the glitz of the strip and for your first trip, I think you'll be wanting to hang on the strip.
A cab from downtown to the strip will run you about $16 each way and that's if you are cabbing to the Mirage or something. If you ever were to go to the Mandalay Bay, Luxor, etc. it would run you over $20.
As far as recommendations on the strip, it all depends how much you want to pay. Barbary Coast is center strip and while it may not be the plushest place around, it is still pretty nice and the rooms are not as expensive as others right near it. But the thing that sells it is the location, you are center strip, near everything.
If you want to go all out for luxury, I am really starting to like the Mandalay Bay. Its a little far from everything else but it has everything you could possibly want in a hotel/casino, including hot chicks abound. The pool might be the best in Vegas and the girls that hang out there are unreal.
For strip joints, I recommend Olympic Gardens and the Spearmint Rhino, both are top notch.