My first professional level banjo over 20 years ago, was a Deering Sierra. I got caught up in the bling dream banjo hype and sold the Sierra for a Deering Calico, which I never liked, which I sold in less than 2 years, and got Gibson ESS which fell apart over the years I played out with it. Last year I’ve come full circle, and found a nice older Deering Sierra at Guitar Center, and I’ll probably take it to my grave. I’m happy, but knowing what I do now, I would still be playing that first Sierra, and never want for anything else.

In my opinion the best value, if you're looking for a flathead Gibson type of sound, is a parts banjo. People often put together banjos with boutique rings and quality parts, and in the end it's not a specific brand so it ends up selling for cheap.

Right now I'm playing a banjo with a Gold Star neck, Cox rim/resonator, Prucha parts, and Shelton tone ring. I picked it up for $1300 and it's as good as anything I've had. 

You can find older Deerings for really cheap sometimes, but the pre-06 tone ring has a sharp bearing surface that doesn't have the typical flathead sound, in my opinion. 

There are used Deering Sierra banjos available from time to time in your price range on the various marketplace websites. The Sierra is a solid professional level banjo, just without any of the bling and fancy inlay. You'll have a full-tilt professional instrument that can hold its own with any Stelling, Huber or Gibson. And if you're not afflicted with BAS (banjo acquisition syndrome) the Sierra can serve well as your lifetime banjo. And an extra bonus: A Sierra will hold its value really well over the decades.

I'm sure other makers have instruments like the Sierra, and I'm not claiming that the Sierra is the only banjo that would meet your needs. I present it here as one solid option for you to consider.

If you find an affordable Sierra be sure - right away - to get it set up by a professional really know how to do a banjo setup.

Are you near the Dayton/Cincinnati area? I know two good shops where you could try out dozens of used banjos to find what you like. I recently checked out about 20 banjos and settled on a 1986 Gold Star for $1500 that I really like.

If you can get to a store or two within a couple of hours that has a lot of used options, it's worth the drive. You can trade in your current banjo too.

Another vote for a Sierra. The newer one’s have nicer inlays, which seems to have softened the price of older one’s a bit. If you care about the aesthetics, they also have the ‘Deluxe’ model, which from the 2010s on is basically a Sierra with nicer inlays, but used one’s sell for surprisingly less. If you don’t care too much about resale value, I’d recommend a Deluxe any day (I am a biased 2015 Deering Deluxe owner, however).

American made vintage Fender Artist, the top choice of several pro bluegrassers back in the 1970s. Used in fine condition, under $2000.

Also top American vintage quality is the Baldwin/Ode Model C. Well under $2000.

If you get a chance try these out. Best buy in the banjo market.

After those, an early 1980s Gold Star Model 100 (made in Japan) would be my top choice.

You have a great spectrum of banjos available at the $2000 spend limit.

Unless you have some aversion to buying a used banjo, check out the classified ads on here. There are 88 five string resonator banjos for sale for under $2000. Quite often, you can get a much better banjo used than you can get if you buy a brand new one.

I recently went thru a similar adventure and I watched a 2017 goldstar gf100jd on Craigslist for nearly a year, that was close to home (within 5 miles) . Finally pulled the trigger and have no regrets at all. I would recommend a goldstar. I agree with Ty Pressly though, if you have a chance to play some that would be better.