If you can afford 100 quid I would hire a guide. I had an afternoon with one and she took me for a 5k run round the imperial palace and then we visited shrines, fashion district, tea room, and had roadside sushi which was amazing.
It’s an amazing city and I wish. Could afford to go on holiday as mine was a work trip. I was advised that Fuji was a bit far to do in the time I had but you should be able to achieve it if you have 8 days.
Make sure you do a shrine and also check out the cosplay peeps that hang out in various places, very very odd.