London-safe, cheap area to stay and tea room recommendations?

Traveling to London, and wondering

A-where is a safe area to stay that is also budget friendly? Would love something close to the Westminster area OR close to east public transport to get there. If you have a specific accommodation recommendation you’ve had personal luck with (or recommend against) it would be great to hear.

B-a tea room recommendation. My daughter may be meeting me there and we’d love to go to a fancy tea in the Westminster area.