@Janice, likely in a church. If you have an outdoor venue you with either need a tent (which can get super pricey) just in case it rains or an indoor back up plan. Are you trying to host 150 guests with 7k? That will likely be super difficult.
When starting to plan my wedding, my goal was to keep the total as close to $10,000 as I could. My venue (ceremony, reception, food, etc included) is going to end up being about $12,500. Granted I picked a golf course, but everything else for my wedding is going to be about $3,000, including all of the last minute things with favors. If you are trying to stay less than $7,000, I would look at sales on things (ex. wedding dress). Many places that go to bridal shows offer big discounts on things; for example, at the bridal show I went to today, David's bridal was offering $50 gift cards for filling out a sheet of paper, a hair salon was offering 50% off of hair styling if you put a deposit down that day. You can also look at using things that you already own (ex. shoes and jewelry).
I know in my area (upstate NY), you can rent houses in a park and have the wedding there for about $500 for the day, you just need to get your own caterer and seating arrangements.
Completely impossible, No (I've got 150 guests & also wanted to stay at 7k, but in reality Im closer to 8k). Now that being said, it is EXTREMELY difficult (cut guestlist if possible). My venue is at a state park and only costing us $208 for 21hrs, my dress is being bought 2nd hand. Having available cash on hand has been the most helpful thing. That way when I've found some crazy good deal I was able to purchase it, without having to worry if it'll be there by the time I can come back for it. I also recommend a lot of DIY if your on a budget... Don't stress out, you can do this!