You can offer both local pick-up and shipping via whatever carrier you wish.
For the first, the payment will be for the item only (and you can accept cash upon pick-up); for the second, you quote an appropriate rate to cover the cost of packing and shipping. You can limit sales to the U.S. and block PO boxes, Hawaii, Alaska and U.S. Protectorates. For large items, you can specify freight and simply indicate a price range within the text (call a few freight services for estimates to various cities).
The biggest problem with running stuff on eBay as local pick up only is…there is no way to block buyers who do not understand that you will not be shipping the item.
Buyers who assume that somehow you are shipping it or will be shipping it or you will arrange shipping for a 5 level chest of drawers and it will be comparable to just a few dollars or free.
Unless the furniture you a re selling is a one of a kind or has some type of inherent value no one is going to pay a $120+ or what have you to get it shipped across country.
If you were a regular seller of those types of items you may at that point be able to negotiate carrier discounts. As is, you do not have access to them.
Unless your items are inherently valuable, listing them here may easily be a fool's errand.