Budget/cheap private lessons

I've visited Japan 5 times on holiday and I've always wanted do an short-term course to improve my Japanese.
When I was single, I didn't have any free time because of a few problems. Now I'm married with a 2 year old and I have more free time, besides work and looking after my child.
My question is, now that I have more free time I was thinking it might be the best time I can go to Japan for 1-2 months with my child (on tourist visa). I know I can't do the intensive/classroom lessons (people will get angry with a toddler in the room). So I was thinking I can find a private tutor and do daily lessons in a cafe or somewhere. I want to improve on my speaking skill.

I'm happy to go anywhere in Japan. Would anyone have any suggestions on private lessons? or have any similar experience?

Thank you!

I would recommend selecting a city/area and searching for a language school, then asking them if any of their teachers (of former teachers there) teach at home on a one-to-one basis. This is just to get access to qualified teachers, not just anyone you can get hold of through language exchange ads and things like that :) Enjoy searching and learning!

For a destination, i suggest you picking the big cities like Tokyo, Osaka, Kyoto... Not only they have many beautiful places to see and visit but also very safe for small families.
Budget should be more than 5000$ including: traveling fee, eating, sleeping place, emergency fee,...

thank you both for your replies. I'll search around for more qualified teachers too.