We went to Hakone for 2 nights at the end of June. It was surprisingly cool and rainy, but it made the hydrangea look stunning. I've stayed at 3 different hotels and one "cheap" ryokan, though my friend booked the ryokan via Rakuten so I am not sure of the name. It was closer to the Gora station. I've stayed at the Kowakien Hotel to be near Yunessun, The Fujiya Hotel, and the Hakone-Yumoto Fujiya Hotel (because it is walking distance from Hakone-Yumoto station and I arrived at 9:30/10:00 pm with a 5 year old.) The baths were nice at the Hakone-Yumoto Fujiya and I liked the location, but the rooms and environment were not impressive. Hakone is a nice option because it has more frequent trains than Nikko and I think is a little closer? One warning, as of today, all of the hiking paths near Owakudani are closed, including the 10 minute one to where you can watch them cook black eggs.
http://www.japan-guide.com/e/e5203.html
I've been waiting to go until you can walk around a bit more than just within the station building.
I really liked Nikko though. I really want to go back, but I'm waiting another trip or two as I don't think I have time. The shrines are stunning and there is a lake with waterfall you can access via bus.
For cheap and easy there is always Kamakura. Most people go as a day trip, but you can certainly stay overnight. I've also heard of people doing Enoshima as a day trip. It might get crowded in July though because the beaches are finally open.
Have you thought about Kusatsu onsen?
Oh, and if you are feeling athletic, you can always climb Mt. Fuji! July and August are the only two months it is open for climbing.
If you have a valid rail pass those days, then you have a lot more options. You can be in Nagano or Karuizawa. I believe there is a traditional style ryokan run by a foreigner and his wife in a small town near Karuizawa. So you could enjoy something a bit more traditional but also have an English safety net. It's possible Karuizawa and area are reachable on a Tokyo Wide Pass or one of the other cheaper passes. I'd personally love to overnight and have more time for Hiraizumi at some point.
http://www.japan-guide.com/e/e6071.html <==the small town with the foreigner ryokan.
