You'd think, having lived in NYC for 35+ years, that I'd be an expert on the city's hotels, but I'm not. However, I can make a few suggestions:
There's a bed-and-breakfast on West 22nd Street in Chelsea, a 10-minute walk from the Garden, called Colonial House Inn. I've never had a friend stay there, as my visitors usually stay with me, but I've passed it many times and it looks fine. I checked their website out of curiousity and a one-night stay on Dec. 4 ranges from $149 (with a shared bathroom down the hall) to $300 with plenty of amenities (including your own bathroom) -- that's very low by NYC standards.
http://www.colonialhouseinn.com
Another option is the Hotel New Yorker, which is a classic (but not super-fancy) old hotel (it was renovated some years ago, so don't let the "old" fool you). It's even closer to the Garden -- just two blocks away (as opposed to 10 for the Colonial House). A friend of mine has stayed there many times, but the price there can vary greatly. If you want to stay there, I'd recommend checking out rates via various travel sites. One caveat: Hotel rates in the city can be higher throughout the Christmas season.
https://www.newyorkerhotel.com
Another option is the Hotel Pennsylvania, another hotel with a lot of history. It's located right across Seventh Avenue from the Garden. I haven't had friends stay there in a very long time, so I can't really say much about it except, when passing by, it looks fine. As with the New Yorker, I'd check with various booking services to see where you can get the best deal (and with some of the quality ranking services too, like hotels.com, to see if my info on all of these hotels is accurate).
https://www.hotelpenn.com
AirBnB is another option. I'm no expert on that service, but I took a quick look for listings in Chelsea. Most of the offerings are single rooms in an apartment, but there are some where you have the whole apartment and some of them look nice enough and at a good price.
If you prefer a fancier hotel or to say in a different neighborhood (all of the above are in Chelsea which is walking distance from the Garden), I'll be happy to offer whatever insights I can about those options.