Kensington Gardens and Palace is a good suggestion. You could have lunch or tea at the Orangery.

I do know that the St. James Sofitel is over your budget. I was going to suggest Ruebens Palace, but I think it may be too pricey also. It's been several years since I've stayed there, but I liked Durrants and it might fit your requirements.

Vicky,

If you're thinking about the Mayfair Millennium, it was a very nice hotel but a bit more of a walk to the metro than I would have liked. Looked closer on a map. There were a few places between the hotel and metro where we had breakfast each morning so it was convenient in that sense.

"<i> . . .a bit more of a walk to the metro than I would have liked. Looked closer on a map. There were a few places between the hotel and metro . . .</i>"

It depends on which underground/tube stations you were using. The hotel is on Grosvenor Sq which is quite close to the Bond St station, a little farther to Marble Arch and quite a walk to Green Park.

(There is no metro in London)