Can I find members who live near me?

I would like to be able to send friend requests to people who live near me.

You can search for clubs based on location.

Some people even go so far as to reveal their location is a forum post.

I have used a search engine with some success to find local players. The caveat there is that the field is 100% optional, anyone can put anything they want there, and many people either leave it blank or put something fake in the location. @CosmicMicrowave, for example, you just have nh for your location, which isn't particularly useful to seeing how local you might be to someone.

NH (New Hampshire) is a small state and I was hoping there was a way to connect with other chess.com members in my state and nearby in VT and MA.

I was actually going to post that NH was a small state but I really didn't now how far other areas might be from your particular location so thought that wasn't a very valid statement for me to make

So is there a search feature in Chess.com? Is there a channel or group I can start?

You can go to Share > Members and search town or state names. That may turn up some. I use Google and use site:chess.com LOCATION

There are also some state level clubs so you can find some that way too under Share > Clubs