Hi, arnearne! I can't make it to any of those dates, but hope you have a great time! I'm not from London but I've visited this great city many, many times, so a couple of questions (then some recommendations) for you...
Firstly (and this is so obvious I feel a bit embarrassed saying it, but just in case you are a travelling newbie, or if you've never been to London before...) where are you flying into and where are you staying? Travel times can take a big chunk out of your time in London, Friday morning can easily turn into Friday afternoon. See also doing it all in reverse on Saturday. London's a big place! And if you're staying somewhere quite far away from Hackney (where The Round Chapel is), add a bit of time to that.
As your desired 'wish list'... I'd recommend Tate Modern, not everyone likes modern art, but I find it quite enjoyable, even if some of it makes me laugh through the sheer pretentiousness of it! Camden... now, a lot of Londoners dislike this place, but I've been going there since is was the most fashionable place in the world for a time in the 90's and so I always try to make it over there when I'm in London. Especially seeing as it seems to being going through massive gentrification these days and will soon be a massive areas of Starbucks and buildings nobody can afford to live in other than Russian money-launderers. The Dublin Castle is one of my favourite pubs in the world, an atmospheric place / total shithole and all the better for it.

I've no idea about boat tours, perhaps a better London mind than mine can recommend something?
So with the information you've given me so far... on Friday, just concentrate on getting to the gig and have a great time. You might find something great that you can recommend to me! Then, on Saturday morning, get the Tube over to Westminster, cross Westminster Bridge onto the South Bank (sadly, you won't see the iconic view of Big Ben as it's getting engulfed in scaffolding for the next four years), keep walking right onto Tower Bridge (a mile or two along) and you'll find Tate Modern halfway along. A couple of good pubs are on the way...

... and then back to get your plane home.
This could all be rearranged with a little more info! Travel time aside, how much ACTUAL time to you have in London?
