IMO Brookline is probably your best bet. A bit of a walk to Fenway but access from the west is easiest. Did a quick look and you can find rooms in the mid to high 200s if that's ok. It could be challenging to do much better than that in September around here without making some real sacrifices though.
I live just outside Boston, happy to give some recs. What are you looking for specifically? Hotel or AirBnB? Walkable to Fenway? More upscale neighborhood or less so? With a little guidance, I can give some recs. Though agree with pjl44 that Brookline is a good option
I stayed in Brookline at an Airbnb in 2018. About 15 walk to Fenway, it was nice and seemed more than safe
2005 - London
2009 - Toronto
2010 - Buffalo
2011 - Toronto 1&2
2013 - London, Pittsburgh, Buffalo
2014 - Cincinnati, St. Louis, Detroit
2016 - Ft. Lauderdale, Miami, Ottawa, Toronto 1 2018 - Fenway 1&2 2022 - Hamilton, Toronto 2023 - Chicago 1&2 2024 - Las Vegas 1&2
There's about 40 of us all staying at The Verb right behind Fenway. We were very lucky to snag room before the prices spiked (and it actually might be sold out now for Sunday and Tuesday nights). It's the best time. We all hang by the pool and blast PJ during the day, and they have a really good post show sushi restaurant. Some of us my have a spare room / bed for Monday and Tuesday night (at a very low rate since we all booked early). If interested, DM me.
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2009 - Toronto
2010 - Buffalo
2011 - Toronto 1&2
2013 - London, Pittsburgh, Buffalo
2014 - Cincinnati, St. Louis, Detroit
2016 - Ft. Lauderdale, Miami, Ottawa, Toronto 1
2018 - Fenway 1&2
2022 - Hamilton, Toronto
2023 - Chicago 1&2
2024 - Las Vegas 1&2