London one night, going to Gatwick in morning..

Trains to Gatwick go from Victoria or St Pancras stations. The ones form Victoria are faster. A bus would be slower and less reliable as it could get delayed in traffic.
You need a hotel within walking distance of Victoria station.

train from Victoria easiest

I have stayed at the Lime Tree and caught an early Gatwick Express. Hotel is a few short blocks from Victoria Station. Lots of amenities in the area - places to eat and purchase groceries, etc. It has been awhile, so I have no memory of cost (have stayed there 3x), but is a nice spot. Looks like you need to contact them and not rely on TripAdvisor for prices. There appear to be numerous options for places to stay in the immediate area.

Thanks guys !! I will look in Victoria station area and a t Lime Hotel

Well Lime hotel is way out of budget range.. ouch.. once a hotel becomes well known prices seem to rise.

Pat, take a look at the Premier Inn London Victoria. I’m seeing a saver rate of 67.50 GBP (non-refundable) for the night of July 22 if you are willing to commit. I haven’t stayed at this particular PI, but the ones that I have stayed at have all been fine.

Laura, thanks for this tip on the PI. I like that chain, too, and this particular one looks to be just across from a park - always a plus.