Royal Opera Covent Garden Area Accomodations Oct 2-10

Hi everyone. I just got tickets to second cycle of The Ring at Royal Opera at Covent Garden arriving next month October 2 and leaving Oct 10. Anyone have suggestions for nice quiet places that aren't too horribly expensive? I'm perfectly fine walking or taking public transportation to the opera and would prefer a place with a fitness center or convenient to a park for a morning run (though I realize that's asking a lot.)