What can I use a a base for displaying large pinecones?

Whatever you wish! If you have a plant stand handy that would look pretty too. Did you have something else in mind?

A basket might be an option.

wooden slab, and drill in from underneath to hold the pinecones. Predrill a larger entry about 3/8 to 1/2" so the screwhead won't scratch what its put on.

If they are very large just set by themselves.

A sparkly charger with a candle stand in the middle.

Buy a cone shaped styrofoam base and attach pinecones from bottom to top to make a rustic Christmas tree. Spray tips with white paint to look snow covered.

Navi....Baskets, bowls, covered cardboard box, old tool box.

I used a large serving dish last year.

You can use a bit if poster putty so they stand up. Will affix to any surface.