Does anyone know where a cheap hotel is in Philadelphia?

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There's a Best Western on 20th and Hamilton just on the cusp of Center City. It's walking distance to the Art Museum and Franklin Institute and is about a $6-8 cab ride to City Hall. That's probably about as cheap as you'll get that close to the city, but I'd still try. There's always the airport, but the cab ride to Center City is a $25 flat rate, and the R1 to 30th Street will probably cost $10 or so and take about 20-30 minutes. There is also a Holiday Inn (and a bunch of others) right oer the bridge in Bellmawr / Mount Ephraim / Runnemede. They're all pretty much <1 mile away from Exit 3 of the NJ Turnpike, and are about 10-15 minutes outside of the city (plus a $3 bridge toll). Seeing as how it'll be May, I'd try for the Best Western first, and enjoy the city--hopefully it will be nice enough outside.

Stay across the river in Camden, New Jersey. It's an easy drive across the bridge into Philly. I would try "Priceline.com" and underbid a two star hotel. You will likely get a good deal if you keep the search to that side of the river.