I don't know what price range would work for you as an individual - but have you considered a coop or condo with a 2nd /3rd bedroom to rent out to a roommate?
There are 35+ for sale in Nassau at the moment with at least 2 bedrooms and priced at $399k and under, in Rocksville Centre, Lynbrook, Hewlett, Glen Cove, Westbury, & other areas
In Suffolk I see 45+ properties in the same category today, including at least 1 foreclosure
It is difficult to outrun the market (I mean by saving money from our paycheck vs real estate equity increasing in a growing market). A lot of people don't give much consideration to apartments, but they can be a great way to get a foothold in the market and house hack until you find something you like in a SFR or multi
I would recommend getting pre-approved for a mortgage as a first step if you haven't already. New York State has several first time homebuyer programs for a below market mortgage rate (& sometimes other assistance). You can buy a coop or multi family with a SONYMA loan as well. If you haven't already you might want to check out their pages:
https://hcr.ny.gov/sonyma
Not every bank offers SONYMA mortgages, and sometimes an FHA (or VA loan if you have served in the military) is the best choice. If you would like referrals for experienced mortgage bankers/brokers, feel free to message me.
Good luck on your search