Is Forest Hills Stadium the only thing you are going to do while you are here? I was there about 3 weeks ago. Traveling from Times Square via the E train subway took about 45 min. So staying in Manhattan or visiting it from Forest Hills is quite doable.
My suggestion to find a hotel around there is to look at the reviews on TripAdvisor.com, Hotel.com & Orbitz. Then when you've narrowed it down a bit, use Google Maps to see if it's easy to get from that hotel to Forest Hills Stadium by subway. The E & F train stop is the closest. The R train is several blocks away by walking. (I don't think there is an M train this summer in Manhattan & Queens. Or it doesn't run on the weekends. Something like that.

)
Here is the Google Map link. It's already set to Forest Hills Stadium and getting there by train to the Forest Hills/71 St stop. Just input the hotel(s) address in the top line and it will give various routes by subway.
https://www.google.com/maps/dir//Forest+Hills+Stadium,+1+Tennis+Pl,+Forest+Hills,+NY+11375/
If you are going there on a weekend, know that there is almost ALWAYS subway detours due to construction on the weekends to either the R train and/or the E & F trains. We usually don't know till that weekend. Yet an E or F train will always go to the Forest Hills/71 St stop as it is a major stop. You might have to take the R train or 7 train part way and transfer to the E or F train in Queens.
Here is a link to find what the various construction detours(s) are the morning of the day you want to get to Forest Hills Stadium, just click on E, F, & R trains to see if there are any detours.
Sometimes Google Maps might even know about the delays that day & re-route the trip differently for you.
http://web.mta.info/weekender.html
Link for subway map:
http://web.mta.info/nyct/maps/subwaymap.pdf