When I can get to a computer I'll post a bunch of hotels close to the park for you. Hard to do on my phone. I can also give you advice on cheap places to eat and other activities in town :) We're pretty hopping in the summer!
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So, the closest hotels are pretty nice. You've got the Clarion Bel Aire, the El Patio, and the Inn at Presque Isle. All of them are at or near 6th and Peninsula Drive, the entrance to the park. A little drive up to 12th Street will find you near a Comfort Inn and the Flamingo Hotel. Other than those, I wouldn't suggest anything else around that area. A little ways down 6th Street to the west, you can find small cottages for rent which also have beach access just a few blocks away, their webpage is http://www.swansonproperties.net/
To eat nearby there are two diners, Takis and the Presque Isle Diner. Both are cheap and have good decent food. Joe Roots grill is pricey. Sara's right at the entrance to the park is also very good for hamburgers and hotdogs and ice cream. There's also a great pizza place called Stevo's, right next to Sara's. I've heard good things about The Ugly Tuna, too.
Things to do at the park: free pontoon boat rides through the marshes, canoe/kayak rentals, bike rentals, fishing, & lots of hiking paths. Many beaches have bathrooms and concession stands, as well as grills (bring your own charcoal). Beach 11 is the only bayside beach, which tends to be shallower and warmer. There are two playgrounds, one at beach 11 and one at the Waterworks beach, near the lifeguard station.
Things to do around town: The Tom Ridge Center across from Waldameer is fun and educational. the Erie Zoo, the Children's Museum (downtown), there are two wonderful playgrounds we like - one in Frontier Park (also a nice place to hang out in general, and they often have concerts and movies there in the summer). and one near the Bayfront Highway. There are tour boat rides both at the Peninsula and down at the foot of State Street downtown. There's a Fireman's Museum near 4th and Chestnut. Waldameer is super fun - as another person mentioned they added a new wave pool this year, and there's no admission to the park, you can just buy tickets and ride a few rides or play at the arcade if you like. Check the Erie Times News the Thursday before you come, there will be a pretty complete listing of activities for the following week in the Showcase section.
*Shameless Self Promotion*
I've lived here my whole life and own a south Asian (Thai, Vietnamese, Korean, Indonesian) restaurant downtown, if you like that kind of thing. Feel free to message me here if you have any questions or want more info on anything. If I think of something else in particular, I will update this post :)