I have a night stand that has a veneer top, that peeled and bubbled,

If you don't have time for refinishing, and who would, when you're selling a house!--consider covering it with contact vinyl. You don't have to match the wood color/look, though that might be possible. You could choose any pattern that is complementary to the rest of the table.

For example, a friend has lovely old wooden tables with marble tops. Perhaps a faux-marble print contact vinyl, or a jazzy print that matches your bedding, etc.

Then, when you have time in your new residence, you can take the time to refinish the tops, if you wish.

Are you taking it with you and want to make it a long term fix, or just for home showings? For home showings only, you can buy some placemats at a dollar store or department store, target or anywhere and just put them on top. Easy peasy.... However if you are going to keep, let me know. That's different.

Have 2 pieces of colored glass cut to fit each nighstand.

A quick and inexpensive temporary solution would be woodgrain contact paper cut to the size of the entire top. Or maybe a granite or marble pattern .

You could also paint just the top in a darker color. Or buy some stick and peel tile sheets that don't use grout.

For a quick fix, because the surfaces are relatively small, removable (peel and stick) wall paper (some can be pricey, though); or for a different look, peel and stick (removable) vinyl tiles. Lots of big box stores and online vendors sell both products.

You can glue another piece of veneer on the top. Should be available at your hardware store.

paint or try contact paper as a quick, cheap solution

How about a piece of granite, marble, limestone, slate... for a high end look? You may be able to find free or inexpensive leftovers at a construction site. If not, contact a tile company or granite fabricator. They alway have a "boneyard"where they store leftovers from previous jobs and can cut a piece to size for you. Best of luck!

I saw you have quite a few responses, but, my first thought was to remove them, replacing them with simple stands that you may have already or can buy very inexpensively. You can only make one good first impression. If you don't want to do that, just cover them with a place mat that coordinates with your bedding, with a lamp sitting on top. No one is going to look at it if it's covered and isn't included with the house, and that will be a quick, temporary fix.

The best long term resolve for it would be to sand and stain again. Then apply a coat of urethane

You all gave me wonderful ideas

Thank you and God bless you all