Methyl's are good (I hope the floating dining room was on a boat; even then it sounds like the Titanic!) Proms in the Park is fun; it's in Hyde Park , opposite the Albert Hall, on the Last Night of the Proms, and has its own programme, but the last bit of the Last Night is relayed to it. The Last Night inside is worth attending for the experience, but you need to be lucky in the general ballot or in the one for those for have been to several Proms.
Myself, I found a really mundane thing the most memorable. When I arrived as a student , my landlady said to get on the top deck of a bus on Sunday, at King's Cross, and travel to the end of the route, so I could know "your London" as she put it. I ended up in Crystal Palace Park. And she was right. The biggest city I knew then was Cambridge !
My partner found an equally mundane thing the best. We had a meal in Veeraswamy's at Christmas, at a table by a window overlooking Regent Street's Christmas lights. She'd done the Last Night and the Royal Opera House and lots of special things of that sort, but she found that magical. Strange lot, these Canadians !