I think the 30th would be a safer bet since we wouldn't have to plan it around other stuff. And actually I've never been to the older side! I tried, once, but my friend and I were about 2 minutes late for the tour we'd booked and the man giving it was REALLY MEAN to us. Then I discovered that the newer side is all lovely and overgrown and crumbly and you can wander around into the dark corners all you like and no one is leading you around talking at you and telling you you can't do stuff, so... I sort of decided I liked that better anyway. Costs less, too!
The Inn sounds fine to me, I'm sure I can work out how to get there but the city's cool too idk anywhere I can reasonably find my way to from a bus or tube stop really!