Onsens near Tokyo

Hello,

I'm planning a trip to Tokyo in a month or two. I want to visit a hot spring, but I'm not sure where to go for just a day visit. Also, we're pretty shy so I'm interesting in finding out which onsens allow bathing suits and might have private areas to bathe before soaking.

Thanks!

I want to visit a hot spring, but I'm not sure where to go for just a day visit.

For a real one day hot spring experience from Tokyo, I recommend Hakone:
http://www.japan-guide.com/e/e5209.html

Also, we're pretty shy so I'm interesting in finding out which onsens allow bathing suits

Onsen are enjoyed naked. There are none where you can wear bath suits, at least not real hot springs.

and might have private areas to bathe before soaking.

You might want to consider a private bath, although, there are not too many private baths for daytrippers. Your number of choice would increase dramatically if you were to stay at an onsen ryokan overnight.