The views of the Eternal City are reportedly spectacular from the Cavalieri Hilton, higher floor rooms at the Eden and the Hassler. For similar views as the Hassler, from certain of its rooms, but quite a bit cheaper is the Inter-Continental Hotel.

In Las Vegas, Strip View rooms/suites at the Four Seasons atop Mandalay Bay are nice....... the MGM Grand SkyLofts seem to be highly rated in the Las Vegas forum though they are not cheap....

In London, the views from the higher floors of the Park Lane Hilton are gorgeous. The park view rooms at the Dorchester are nice, as are the Studio Suites of One Aldwych. The latter two hotels are over the OPs budget unfortunately.