Do you have any suggested routes?
Just head south; it's 500 miles but you can go 80 mph for most of it. From Reno, you can drive south on US 395 and go through Smith Valley and Yerington, which is the prettier drive, or you can go east on 80 to Fernley and then had south and wind up in about the same place southeast of Yerington. Stop in Goldfield and check out the old restored hotel. Other than that, drive fast and enjoy the scenery.
In Reno, save your money for Vegas. Reno is a shell of its former self and I wouldn't waste a dime gambling in what's left of downtown. Go to the Peppermill on So. Virginia Street, it's where all the locals go and the odds are better. Food is really good there, too. For breakfast, have someone give you directions to Deux Gros Nez, go there and act like you live there; it's a fascinating hip local diner (or it was for many years; ask about it). If you are staying downtown and have to eat there, run over to the Eldorado hotel; they have the best casino food, and their Italian if really good (they own the Ferrari Carano winery in California).
Reno is a pretty town this time of year, still moderate weather, leaves have turned to gold and red (unless you get a frost, then they're all barren). The University of Nevada campus is something to see; park there and walk it. Downtown has a river walk under construction, largely finished, worth a stroll. There is a pretty good antique car museum downtown, too. Tahoe makes a nice side trip and takes a good hour to get there; go up Mt. Rose Highway and come out at Incline; from there, head west towards King Beach and take the road (267 I think) to Truckee. That's a nice drive and Truckee has some nice watering holes (local color can be soaked up at Bar of America).
Then take the freeway back into Reno.
If you are renting a car, consider a four wheel drive; the road to Vegas takes you over a couple of small summits, and it could snow in northern Nevada that time of year. If you don't want to fly, Southwest Air and some others fly to Vegas from Reno every hour; if you book now, it'll be pretty cheap.
Now Vegas, baby, that's unreal. Go all touristy and gawk at the theme hotels: do not to miss Bellagio, Venetian, Paris, Wynn, Caesar's Palace, and there's more, but if that's all you have time for you will be amazed and entertained. Go online, see a map of the strip, memorize where everything is, and get acquainted with the town. If you want to gamble, go one long block behind Bally's and find Ellis Island; it's a local dive but the odds are much better there and you might even win some money. Food and drinks are really cheap there, too. But the big show is on the strip so if you're only there for a few days, let them park your car and just walk from place to place (or use the Deuce, a bus that runs up and down the strip): there are also trams between some hotels and a monorail that is more expensive and not that easy to get to from many places.
Have fun!