I would recommend looking into non-traditional venues. Instead of searching for "wedding venues" look for places like parks, fancy restaurants, etc, that you could use instead, then call and ask their policies and pricing! I have heard of people getting married in botanical gardens, local parks, fancy restaurants/bars, etc. Good luck!
The most cost effective venue I found in my area was an "all-inclusive." So you could try googling "all-inclusive wedding venues in city, state and see what comes up. It really depends on how small you want it. I definitely agree with Brianna, look for non-traditional places! What area are you in?
Do you have any other friends that have gotten married in the past couple of years? If so, you can ask them about their venues. I didn't even tour venues. I attended a friends wedding a few years ago, and fell in love with her venue. I never knew it existed until I went to her wedding. It was in my price range too, so I made the decision that that was our venue.
Thank you! I ended up using someones comment from Reddit and used an Airbnb place that was big enough for my intimate wedding!! super excited.. Ceremony, reception, and a place for the fiance and i to stay after the big day!