I assume the pet is a dog? Many US hotels allow dogs but not e.g. cats so you'll need to check individual accommodation policies. The reliable and long-established https://www.booking.com has very extensive US hotel/motel listings. It has excellent mapping, excellent rates and a 'pet-friendly' filter which you can use to search for suitable accomm in any specific location. Use https://www.googlemaps.com to follow the suggested fastest route below to see if it's suitable for you. Journey length is just over 2500 miles, driving time is 38+ hours dependent on traffic congestion, roadworks etc. There may be some tolls. I've made a few pet-friendly accomm suggestions near the road you'll be travelling on after roughly every 10 hours of driving (more than 10 hours a day is very unsafe unless you have a co-driver). Booking.com will give you lots more. 1. Take the I-75 (N) from Naples (Florida) to J435 where it meets the I-10 NW of Lake City (Florida). 2. Left onto the I-10 (W) and follow it past Tallahassee and Pensacola towards Mobile. There's a Hampton Inn at Daphne east of Mobile and a La Quinta Inn a little further west on the I-10W at Tillmans Corner. 3. Continue on the I-10 (W) past Baton Rouge and Houston towards San Antonio. There's a La Quinta Inn about 40 miles east of San Antonio at Seguinand a Comfort Inn, a Best Western Plus and a Days Inn off the I-10 as it enters the east of SA. 4. Continue on the I-10 (W) past El Paso towards Tucson. There's a Motel-6 and a Quality Inn at Benson, about 45 miles east of Tucson and plenty more options off the I-10 as it passes the city. 5. Stay on the I-10 (W) to Palm Springs