We stay at Zephyr Cove RV park frequently over the years (our motorhome is pictured on their 40' site description from 2002). It is a short walk through the resort to the beach and wooded trails. We also have enjoyed the onsite restaurant over the past 13 years. You will have peeks at the Lake from most campsites.
Try not to get a site near Hwy 50 near the entrance to the park.
Tahoe Valley is a bigger rv park, but not close to the lake. After June, the park gets dry and dusty in our opinion. But, they fill up all 400 sites on major summer holidays.
These are the only two that meet your stated requirements near Lake Tahoe that we could suggest. There is one more on the West side, but it is small and does not accept pets.
The prices at both parks have risen dramatically recently. Location, Location and a short summer season.
Dean
95 CC Magna, Jeep GC