Given this weekend is also the start of the US Open (Sorry!) Hotels can be pretty salty. I've researched a couple in Flushing and one in nearby Bayside. I would avoid Jamaica. If you're very price sensitive, the lowest I've seen nearby are at JFK Airport.
We do have a Room Block at the Fairfield, but it is not the cheapest option.
The rates below reflect when I last researched it on April 3rd. I recommend booking a hotel as soon as possible, with a refundable rate in case your plans change or if I’m able to secure a block.
I will warn this hotel is a bit in the middle of nowhere. It's across from the Police Academy, and near the ConEd Repair Depot. It's not a bad area, just nothing around it.
The Room Block is $339 for a King, $369 for Two Doubles. It's not the cheapest option, but it's a solid option between a basic hotel at a lower cost, and the higher priced options, all below.
I think they're offering free parking, space limited
You will have to put a deposit down for the first night on a credit card. If you need to cancel, you need to do it at least 14 days in advance. Details on their website.
Room block is good until July 21
https://app.marriott.com/reslink?id=1775679000462&key=GRP&app=resvlink
This is a fairly basic hotel, but had good reviews and the lowest price I could find in Flushing
You will need to join Wyndham Rewards for this rate, but it's free to join
The rate is for AAA members. This is also a good location, next to our apartment. Probably the best location if you're driving, because you can either park at Skyview or Tangram garages, which are self parking for a fee
This is in Bayside, which is about a $35 uber to the location. It's a decent alternative to get away from the US Open chaos