This is a lot about what you want to spend but then again there is nothing really high end out there. Also, don't wait to book your room. My son played at Baseball Heaven for many years and did two head first's there too. We stayed at Fairfield Inn in Medford a few times. Very easy onto the highway to BBH in 5 mins max. It's not high end but much better than the comfort Inn next door. You will see the college coaches in both these hotels but they are usually trying to be incognito. I 100% would recommend Springhill Suites in Yaphank, it's half a mile from baseball heaven and probably about 5 years old will sell out fast. Again not high end but certainly more than good enough for a baseball weekend. It's the closest to the facility. If you don't book early enough you will be out by MacArther airport which is not bad or over in Stony Brook in the Holiday Inn Express which is fine but quite dated. The rooms fill up quickly. Now for the one question you didn't ask, where to eat - my recommendation is Cafe Gia. Very good, reasonably priced Italian just around the corner from the facility. Good luck at Head First! It's the best run of the bunch in my opinion too.
Oh - 100% avoid Jakes 58 Casino Hotel. May sound like fun but run away. used to be a good decent hotel about 20 mins from BBH when you were late to book but since it became a casino (slots only) its impossible to park, loud and filled with smokers.