Points of interest route

You'll be taking I-10 along the southern coast. There are interesting places and restaurants along that route. Check out Biloxi and New Orleans. Continue on I-10 through Houston to San Antonio. The River Walk in San Antonio would be a pleasant place to pause for a meal and to stretch your legs.

You want to turn off I-10 at San Antonio because it I-10 is just a Boring (with capital B) desert highway across west Texas. Take Highway 90 out of San Antonio through Del Rio, Marathon and Alpine (Texas). It is a very scenic route. If you can time it, plan to stay at the historic Gage Hotel in Marathon. If time permits, take a side trip from there into Big Bend National Park. After that you'll merge back into I-10 and continue on to the west coast.

Santa Fe (New Mexico) would be a good stop in New Mexico. The Grand Canyon National Park would be an awesome detour when passing through Arizona. 

I've not driven from Tampa to San Francisco but did Tampa to Austin several years ago. The fastest route is I-10 as mentioned by RosalieAnn. I would prefer the alternative route on I-40, and make a special stop at Grand Canyon National Park.

After Grand Canyon, I would make my way on Route 66 to Seligman, Kingman, and Needles, eventually to Santa Monica where it ends. Finally, Santa Monica to San Francisco. Take a look at this article by LA Times on A trip on Route 66 proves to be unchartered territory for a master planner.

This article may be helpful if you're planning the Route 66 route: https://www.historic66.com/california/de1.php

Besides Grand Canyon and Route 66, these are the highlights to add on to RosalieAnn's great suggestions:

1. New Orleans

2. Austin

 Second Part - Austin to San Francisco Then you can follow I10 from Austin to Los Angeles and hook up there with I-5 and go right up to San Francisco  But you could deviate a little bit and go to Carlsbad Caverns National Park and once you got to the LA area you could go up California 101 to Monterey

First part - Tampa to Austin - If you are in a hurry to get from Tampa to Austin the quickest way is to take I-10 across.  You can stop in Pensacola and go to the National Naval Aviation Museum there and then go to The Fort of Colonial Mobile Baton Rouge and visit the new capital (and also the old one if you want) and go through Houston  with maybe a stop at the Big Thicket National Preserve where they have three kinds of carniverous plants.  But if I were doing it, I'd follow US 98 around the Gulf and visit Saint George Island, Panama City (Florida) and Fort Walton Beach before I got to Pensacola.

Make a stop at the Grand Canyon National Park!!