The non-airline credit cards that offer lounge access generally offer it through Priority Pass (Diners Club is an exception, but their US cards aren't available to new cardholders). I'd check out the lounges for your normal airports over at https://www.prioritypass.com to see if you'd even be able to use them given your travel habits; the AF lounge at SFO, for example, only allows Priority Pass users if they're leaving from the same concourse.

As for pricing, UNFCU has a $50/yr card that offers Priority Pass, but underwriting is pretty strict. (I was denied with a >800 credit score and >$100K/yr income, if that tells you anything. They counteroffered with the no-AF Azure card instead.) I'm also not sure how many guests you'd be allowed to bring in without a fee, if any.

Other than that, the Chase Sapphire Reserve is probably the best deal for Priority Pass at the moment. It's effectively $150/yr after the $300 travel credit and allows unlimited guests for free (for now at least, subject to the individual lounge). It's also easier to apply for, assuming you're under 5/24 of course.

The downside of those is that you don't get hotel status, but they're inexpensive enough that it's feasible to combine them with a hotel card to get said status.