Hey thank you for the reply. Unfortunately I'm well below 5.5, more like 3.5.
As for places to play tennis.. I would google or search old TT threads. I don't know where you usually play but court times are VERY hard to come by from what I hear especially in the city. There usually large waiting lists. You could probably find courts on the outskirts of the city with a shorter waiting list or none for approximately 200 yen/hour = about $3/hour.
For places to stay, it really depends on your budget. There are many hostels in Tokyo as well as luxury hotels. I'm not sure about near the tennis park area. If you like busy areas, I would recommend staying in the Shibuya, Shinjuku, Meguro, Ebisu, or Roppongi areas for example. Roppongi is one of the most foreigner populated areas in Tokyo if that's your thing.
Also if you're looking to check out tennis equipment, check out Windsor Tennis or Eddy's Tennis in Shibuya. The rackets are more expensive considering the dollar to yen conversion but there are a ton of selections; especially at Windsor. Keep in mind these shops are Japanese run and owned so you will need to know some Japanese if you don't exactly know what you want.
Perhaps we could meet up for drinks if you have time? Japan is a very meet, chill and drink culture so I hope you don't take offense to me asking. I'd be very interested to hear your experiences as a 5.5 player.
Cheers and enjoy your first trip to Japan!