Yes, you can park at the Park-inn. It's like £4 for 1 hour...take a bit extra just in case.
I was there the other week. Pay machine I used it was £2 per hour, £4 for 2hrs but I guess if you're going for 1hr punt, perhaps pay for 2. There are a couple of coin machines as an alternative to paying by phone and it going on your bank statement.
When you go in the entrance, it looks like the spaces are all taken but if you continue round the side to the back of the building, there are more spaces.
Also, it is a fucking,
massive rabbit warren in that hotel. To add to the potential confusion, the room numbers are 4 figures.
I spent ages walking round the hotel trying to find a room that I'm not sure existed and missed my booking so no punt and a totally wasted 3hrs.
I never worked it out for sure, I could have got it wrong because the hotel is split in two, with lifts on left and right, though Tony could perhaps clarify.
In short, get clear directions from any WG there. I prefer the hotel the other end of Bath Road - so much easier in every way.