You could also consider the Victoria Premier Inn.
Lime Tree is a popular recommend on this forum.
The neighborhood IS Belgravia.
Perfectly fine area to stay in.
Also in an earlier post you asked about safety. I’ve been traveling to London since the 70’s. Usually solo. Walk or tube back from late night theatre performances, out for pre dawn walks in Hyde Park, have tubed back from Westminster to Chiswick at 10:30pm this past December then walked solo to the Chiswick Premier Inn.
Safety has never been an issue for me in London or the suburbs.
Lastly, Big Ben is the bell, it’s in Elizabeth Tower. Do know that it is presently in scaffolding so the iconic photo op won’t be what you imagine.
Use the tfl.gov.uk website to help you get around. Get your Oyster Cards when you arrive.
Lastly, it’s a very easy stroll from Parliament Square
( Parliament, Westminster Abbey, Churchill War Rooms) via Birdcage Walk through St James Park up to the Palace. You can also walk from there up Whitehall past the Horse Guards and #10 Downing Street to Trafalgar Square and the National Gallery. From there easy stroll into Covent Garden. London is a very walkable city.
As far as a park to enjoy tube to Lancaster Gate Station, exit. Turn right and cross Bayswater Road at the light and walk into Hyde Park and the Italian Gardens. The Serpentine is right there. Princess Diana Memorial fountain is a short walk past the Peter Pan statue and just before the Lido.
If you want a bigger park to enjoy, tube to Hampstead and follow the Flask and Well walks into the Heath. Nice neighborhood and the Heath is gorgeous!