Here is some infor on last year's jumior programs at the Tennis HOF,

I'd give them a call and see what they are offering this year:

tennisfame.com/play-tennis/…junior-programs

I believe since you will only want a week, you'd pay the "drop in rate" per day, as opposed to the (4 weeks x #of days) rate.

In terms of locations Jamestown, the island just across the bay from Newport is possibly the area's most stellar summer community, where you could rent a house for a week or two. It's a quieter alternative to Newport, although the village at the harbor has several cafes and nice restaurants. You can hop on the water taxi to get to Newport, or just drive over the bridge.