Best thing to do is bring them to a bank. But this is not your only option; I will offer one other suggestion; Which will require some effort on your part.
Sort the pennies into two piles, pre-1982 and post 1982. Pennies minted prior to 1982 are solid copper, and worth .03 cents each to a copper stacker, who might be interested in buying them for future sale. (anything severely damaged will have to go to the bank, or possibly be advertised and sold on Craigslist in bulk for face value plus a small premium, if you find a buyer)
Everything newer than 1982 goes to the bank, to be exchanged for cash. (Unless you search for 2009 pennies, which are more valuable because it was a low mintage year, but be aware that only ones in good condition can be worth as much as .30!
If possible, divide the remaining pre-1982 pennies into piles based on their dates. Hopefully you will be able to read the dates and identify Wheat pennies which may have a premium.
At this point, you can sell the pennies – always disclose their less than pristine condition – in a bulk sale on eBay, Facebook marketplace, or Craigslist. If you get .03 cents for them, you will triple the face value based on the value of the copper content in the pennies.
Now remember I suggested you divide the pennies based on date, this is where some work comes in; get a book like “strike it rich with pocket change”
and determine if you have any collectible/valuable years. Pull these out and sell them separately, in a lot or individually depending on how much time you have to invest in the project. You may have to discount them due to condition (never clean them, always disclose that they are damaged and less than pristine). At this point a dealer or serious coin collector might make you an offer.
While This is a lot more work than dropping them off at a bank, you may recoup a decent return on your efforts if you have some key dates on your older coins, or “mint errors”.
If you are fortunate enough to have a teenager available, this will be an excellent way to motivate them to think “outside the box” and earn some pocket change in the process. (this may not work on some teenagers).
In any case, best of luck sorting and hopefully selling your pennies at a profit!