For reference, here is the site for searching for building permits in Douglas County Nevada (since Tesla says it will be in Stateline). You can search for Tesla in the Applicant's Name (right now finding only the Gardnerville site) or you can enter 514 (and later 515, 516 etc.) under Permit or Application Number to see the most recent permits in the system. The list can be narrowed down to just those which have no issue date or have an issue date after the application date since a plan check will be needed.
If it's really gonna be on the Nevada side, the most likely spot would be the Harvey's parking lot between Harvey's and Lake Parkway. I suppose they could put it at Montbleu or somewhere near the Kingsbury Grade intersection, such as Lakeside, but those would be fairly mediocre locations.
The better locations would be on the CA side. I know some here mentioned the "Y," but I think the better locations are closer to the state line.
One obvious location would be the "South Y Center" where Emerald Bay Blvd. and Lake Tahoe Blvd. split. IIRC, NRG will be installing some dual standard chargers there. ChargePoint will also be installing a pair of their new DCFCs on Heavenly Village Way with CEC grant funds. Both of those sites should be open this year.
Personally, I would vote for something in or near Meyers. Too frequently traffic just crawls through SLT, even if one detours via Pioneer Trail. Congestion is the norm at Stateline.
Highway 89 continues south to Alpine County and highway 88. From late spring until the first heavy snowfall, highway 89 is an alternate (and better in my opinion) route to get from SLT to US395 via Markleeville and Monitor Pass.
+1 We had our first Tesla trip to Tahoe in late March, using the Reno charger and staying at the Best Western by the Brockway/Tuckee charger. We skied Mt. Rose and Squaw. Our Tesla will not go to South Shore until that charger is built.