If you get the chance, check out NOPI in Soho. Popular amongst locals and able to provide a decent meal for the price, you'll get the quality cooking you'd expect from the even more popular Ottolenghi in Islington, combined with a chic establishment with a cool, pleasant atmosphere.
If Big Ben isn't your thing, but you're still looking to get a taste of British tourism, why not check out the local cuisine? The real local cuisine, not the posh restaurants that tourists seem to love, but the dodgy holes in the wall that really speak to London's under-the-surface culture. London also has arguably the best street art in the world with hotspots like Leake Street, Camden, and East London.
Earl Gray, and not just because Q from Skyfall fancies it. It's a tea that will go with just about anything, and is quite popular not just in London but all throughout Europe. It's hard to beat a gentle but full flavor like Earl Gray, and because of its popularity it's far from expensive. Dean Street Townhouse offers up some of the best afternoon tea around, whether you go with Earl Gray or anything else.
There's the El Corte Inglés in Malasa?a and the Plenilunio in San Blas. These are two of the more popular shopping centers, and will probably have enough to keep you occupied for at least a few hours each.