Highgate is on the northern line (see tube map) on the north bound not far from camden town, better to catch tube, cheaper and quicker xx
As for hotel, go on http://www.hotel.com or google hotels in highgate london, I’m sure you will get some..
I didn’t bother with overnight stay. I left about 6hrs later when my bf came to pick me up after op. Its more discomfort..
Xx