Gf & I have never been, but planning to go in June. Emerald Bay State Park looks awesome. Other than that, what are the must do things or places to go while there?

What are the best places to stay that don't cost a fortune?

Finally, looks like flying into the Reno airport & driving 45 minutes or so to Lake Tahoe is the most cost effective way to go, correct?

Emerald Bay is very nice, plan on going early in the day if you can, expect big crowds.  Check to make sure they are open and see if you need a reservation.  We always get a Barnyard Massacre on wheat crust from Lake Tahoe Pizza Company when we're over by Emerald.  Squaw/Olympic Valley can be really nice to visit in the summer, and is also over on that side of the lake.

Tahoe is a really touristy place in general, its hard to get away from that, especially in summer.  The hike in beaches on the east side of the lake can be great, but you have to be up there on the trail early, Skunk Harbor is pretty fun.  The Flume Trail is a good hike/bike also on that side of the lake, amazing scenery.  If you like touristy stuff the Heavenly Village is great for shopping and food.

Cheap places to stay don't really exist at Tahoe, check the usual Airbnb stuff though just in case.  Its only about 20 minutes drive from Carson City to Stateline Tahoe and about the same from Minden, you'll pay less for a nicer room down there.  Reno-Tahoe is your closest airport, and the drive up Mount Rose or up 80 and through Truckee are great beautiful drives on their own.  Have fun.