Considering a "last minute" trip to Madrid, Seville, Granada and Cordoba for about 10 days beginning of May. Do you think it will be crowded already, is it too late to secure tickets to some of the attractions? Any recommendations for hotels and/or rentals? Thanks in advance.

Madrid Open tennis tournament is on from 22 April to May 5th.
Also , May 1 is a holiday ( in some place May 2 as well)..it tends to be a busy time .

What's the nightly budget for hotels/apartments?

We are thinking, now, of flying in and out of Seville and staying in the Andalucia region (not going to Madrid) at around $150-175/ night. Is that reasonable. I assume we will need a car.

virginiafish,
If you only plan to visit Sevilla, Granada and Cσrdoba you can reach these 3 cities of the Al Andalus triangle by high-speed rail (ditto to reaching Mαlaga or reaching Cαdiz by MD train from Sevilla). For exploration of the white towns of the Mαlaga or. Cαdiz province, you will want a car, picking up after you leave the city and dropping it off before entering your next city to avoid getting caught in the Moorish maze of these cities's historic quarters.

Yes, May in the above cities will be busy. You should secure your Alhambra tickets well in advance.

Lodging for between 150-175 USD a night? Do a lodging search for each of your destinations on booking.com changing euros to dollars at the top of the page and on the left, select other parameters you need (you'll definitely need a/c). Scroll down and sort by "top reviewed" rather than "our top picks for you". Booking.com lists hotels, guesthouses and apartments.

You should have plenty of options within that dollar budget in Granada and in Cσrdoba, except during the Cσrdoba Patios Festival, held this year between May 2-12.
Sevilla hotel rates will certainly be the most expensive. Here you may want to opt for an apartment.

HI all, Cannot tell you how much we always appreciate your sage advice. Getting a little concerned about the number of tourists (which, of course we are, too) in May and thinking we should look at this for a more off-season time. Your help is valuable! Thank you!

Yes, virginiafish it will be very busy in the south in May and also it will be beginning to warm up!

Virginiafish, We just returned from a similar trip. We took the Alsa bus from Granada to Sevilla and it was fine. It offered many more departure options for us. Just another thought.