Are there any free or inexpensive places to park in Atlantic City near Casinos and in Philadelphia near Independence Hall?

There's nothing as "free" parking in Philadelphia, as residents usually pay $200+ per month for parking in the city.
If you're visiting on a Sunday, you can find street parking as you don't need to feed the meters on sundays.

For the Atlantic City casinos, I definitely recommend parking at the casino garage. They charge a fixed rate of only $2 (or maybe $5). Much safer than parking on the street and then walking to the casinos, IMO.

With a bit of hunting you'll be able to find a parking meter within a few blocks of Independence Hall, a quarter for 15 minutes, usually a 2-hour maximum but you can go back and "feed" the meter before it runs out. Don't park at the short little meters--they're for handicapped. There are many parking lots, the further from the main attractions, the more affordable. Some have weekend specials or evening specials.

If it's a typical Sunday in Philadelphia, MOST meters will not be charging, but some will. Check to be certain. The problem is, there won't be any spaces available with free parking anywhere near Independence Hall. Your best bet is to use public transit or plan to park nearly a mile or so from Old City.

Atlantic City parking is between $2 and $10 for the casinos, depending on which one you go to. But, if you get a receipt on the way out, you can park free in any other casino garage during the same day. So, if you're like me and spend time on the boardwalk and then go out to the marina, you only pay once. Avoid Caesars--I believe they're the most pricy at $10. I normally park in Showboat for $4.