You might consider holding off on the turntable until you can save a little more (and accumulate some research info.) and instead look at different cartridges. I know this isn't what you asked about and I apologize for going in a different direction, but I wanted to share a recent experience I had with a Technics turntable I got from Circuit City over 10 years ago. It was in storage for several years until Christmas when my teenage son mentioned he wanted a turntable. I thought we would try the old Technics first. I had long since removed the Shure M92e cart that was on it and gave it away. I never liked the Technics/Shure combo. I ordered a Grado Black P-mount cart ($40) for the Technics and WOW I was surprised by the big, full sound and deep bass. Have you been using the same cartridge since you've had the Sony? Is it p-mount or standard (1/2") mount or a Sony proprietary mount? If the Sony tonearm accepts p-mount or standard cartridges then you have some options.

IMO, it will take some time to find the right used turntable for $200 or less. It can be done, but I would suggest familiarizing yourself with brands and models. This would include learning about models that are no longer in production and from some manufacturers no longer in business. Checking out used Duals and Thorens on eBay and Audiogon may be a good place to start, but you'll only be scratching the surface. Then, you have to decide whether you want to roll the dice and buy from an e-seller based on pics and the seller's representations and feedback. You'll also need to make sure the seller knows how to pack & ship a turntable. If you buy used locally, it could take forever to find a good used table depending on where you live. Then, when you do find the right used table, you might have to buy a new cartridge for it. This sounds like a lot of work but the search can be very interesting and fun.

As far as new tables go, you probably need about $400 to get into a belt-drive turntable and cartridge to hear improvements over the Sony. And then the improvements might not be significant enough to justify giving up the convenience of auto-return and auto-shut-off assuming the Sony has those features (and you like'em). It really depends on your own hearing. Some models to consider are the Pro-ject Debut III and Music Hall 2.1. These come with cartridges for around $300 but you can do better than the supplied cart for around $100.

Next you would be looking at tables anywhere from $450 to $650. IMO, this is a solid entry point. Models include the latest RM series entry from Pro-ject, the Music Hall MMF-5, the Rega P2 (if you can still find one) and at the high-end of this bracket - Rega P3. The Pro-Jects and Music Halls come with carts, while the Regas don't. (My estimated price bracket may be off a little because my research is old, but as an example www.upscaleaudio.com still has the Pro-Ject RM-4 with cartridge for $479. I think this model has been replaced by the RM-6 which is probably higher. I'm also going on memory with respect to the $650 price of the Rega P-3. It may be more now. I noticed some import prices going up a couple of years ago when the dollar started dropping.)