Venue suggestions?

That's tricky, because I don't think anyone can 100% guarantee that they'll be able to have more than 10 people this summer. Do you, or anyone close to you, have enough space at your home to host your guest list? Even if you don't have enough indoor space, if you have a yard (or can borrow one) you can probably rent a tent.
A lot of summer weddings have been canceled or postponed, so you might still be able to find a tent, caterer, etc. even though it's kind of last minute.I don't know the area well enough to give specific recommendations, but people often recommend renting out restaurants as a relatively affordable way to host a wedding because they'll usually only charge you for the food so you don't have a separate venue fee. At least where I am, it seems unlikely that people will be ready to go out to eat all the time when that becomes an option, so many restaurants will probably be excited to have the guaranteed business.

As PP said, I'm sorry, but all venues are likely to say this to you. If you are upstate, and you can find an outdoor venue, you *might* be able to have more than 10 people, but it'll be hard to promise. Additionally, it's hard to say that international travel will resume any time soon, without mandatory quarantines.

That said, take a look at the "venues" tab above. Limiting your search to outdoor venues is your best bet.