You have a Meucci Jim Rempe JR-3 cue from the Meucci Jim Rempe Series 2 (circa 1990s I believe). Meucci made an earlier line in the 1980s I think (or earlier?) but yours, with the flat black rubber butt-cap, is from the 2nd Jim Rempe Series from Meucci. 100% sure on that. He said he won it in 1980. That's doubtful. Maybe he said "eighties"? As in 1989. Even that seems early for this series.
The 2nd Series Meucci Jim Rempe JR3 is sometimes also known as the Meucci Jim Rempe Chain Link cue. The "chain link" design was later used in a non-Jim Rempe version from the "Meucci Series" cues. It was the "Meucci M-11 cue" or "Meucci Series M-11 Chain Link cue".
Value varies widely, based usually on condition, but there are lots of them out there, and they aren't hard to get. Ranging from $150 for badly damaged, to $1500 (which they wouldn't get). A few pristine ones somewhere in between.
If you send it to the Meucci Factory, they do beautiful restorations. Google Meucci cue restorations and you'll see some amazing before and after.
Here is a sample of a few I've seen over the past 10 years, and their asking prices. Keep in mind some of these prices are from auctions which were between 5 and 8 years ago, and some more recent.
Hopefully these help, and at least you have information to continue a more in-depth price analysis.
$1500 (on eBay right now, and they'll never get that price).