Ok, so the CLD-2080, assuming everything is working properly, is a pretty solid player. It doesn't have a lot of the features of the later 90's players, but you need something pretty high end to get significantly better. Keep an eye on Craigslist, as you might get lucky and find a high end player cheap, but otherwise I'm basing my pricing on recent ebay prices, which have been increasing lately.
First of all, if you see a CLD-97, BUY IT. It's the best player you can buy without going into retarded money territory. I paid $300 for mine, but they're going north of $500 on ebay now. As much as I love it I wouldn't pay $500 for one. The only downside to it is that it doesn't have a Dolby Digital RF output if you care about that unless it's modded. The newer version, the CLD-99 is a solid player with Dolby Digital but the image quality is a little inferior to the 97.
For the $100-200 range, there are a couple of players I'd keep an eye out for.
DVL-700 is a seriously underrated player. The DVD portion is awful but the Laserdisc side is excellent. It has every audio output possible, and it has one of the cleanest videos you will find. CD audio output is also better than any player I've used with the exception of the CLD-97 and the LX-900. The drawback to the DVL is that it has built in DNR that you can't turn off. This is pretty good if you hook it up to a SDTV, but not so great if you use a HDTV or a scaler of some kind. This was my first player and it will always stay in my stable. The other DVL models like the 909 are still solid LD players, but not quite as good. They are also creeping up in price, don't pay more than $100-150 for one. They are above average but they're not top tier.
Panasonic LX-600 is around the same class as the DVL, but the image quality is a bit better. it's a very low noise player so the image is pretty solid and a little bit sharper than the DVL. I use this as my secondary player connected in my office right now. The downsides to the Panny are no Dolby RF output, and parts aren't readily available for them. The good part is that since Panasonic doesn't have the same name as Pioneer in the LD world, you can sometimes get them for a steal. I paid $80 for one player, and $100 for a second. (yeah I like this player enough that I bought two.)
Also keep an eye out for CLD-700 series players, particularly the CLD-703 and CLD-704. They used to be the best players you could get for the money (better than many Elite models) but the word has gotten out and the prices have risen. $250 for one is a joke, but sometimes you can get lucky.
If you go up in price a bit, keep an eye out for a Panasonic LX-900. It's very similar to the LX-600 (they share 90% of the same parts) but it has a better video and audio section. Panasonic built this to compete with the CLD-97 and they did a damn fine job. On high quality discs the LX-900 is in the same class as the CLD-97. Not quite as good, but really close. On bad pressings, the LX-900 has a noise reduction setting that works wonders. It is the only player I've ever used that actually has good noise reduction, able to filter a good bit out without taking a big hit to detail levels. Even the CLD-97 has garbage noise reduction (which can be turned off thankfully.) I currently have the LX-900 as my main player as my 97 needs some maintenance. I paid $240 for mine which is a decent price but not exceptional, but sometimes you can get really lucky. A LX-900 recently sold on ebay for $99 shipped, which is crazy.
Like I mentioned with the other Panasonic, the big issue with the LX-900 is the lack of available parts if you need to fix it. It's a good idea to pick up a cheap LX-600 to use as a parts machine if you get a 900. Almost everything is interchangeable. If you look at Pannys the LX-600 and the LX-900 are the ONLY ones you want to look at, most of the rest of the Pannys are garbage. The LX-670 might be okay since it looks similar to the 600 but I don't have any personal experience with them.
Now, all this being said, even the best laserdisc player is still a laserdisc player, and most players are going to look like complete shit on a HDTV. Keep that in mind. They are best used with a HDTV or a scaler of some kind. If your 2080 is connected to a HDTV, a top of the line player really isn't going to look much better. They still look great on SDTVs that have great comb filters though.