Best free things to do in Tampa?

Hi Katie! There are many places to see in the Tampa Bay area. I'll suggest you to start from the historical area (downtown and nearby) of Tampa. Stretching 2.6 miles along the Hillsborough River, the Tampa Riverwalk has been named one of the top 15 riverwalks in the U.S. Head “down by the river,” and you'll discover a fantastic array of family-friendly parks, museums, water activities, festivals, dining options, and bars.
If you need to park your vehicle you can do it at University Of Tampa (for free). It will be at Frederic H. Spaulding Dr and W Kennedy Blvd. This private university is a MUST to see. Will be your first "thing to do". The architecture is Moorish Byzantine style and has beautiful gardens.
Here you can visit the Henry B. Plant Museum: the museum houses original hotel furnishings and art objects collected by Plant from Europe and Asia. Now you have to go to The Riverwalk. Take a slight left onto W Kennedy Blvd, continue straight, walk over the bridge heading downtown. Once there you can visit the museum of arts located on 120 W Gasparilla Plaza. The Tampa Museum of Art invites everyone to Art on the House every Thursday evening from 4 – 8 pm for Pay-as-you-will admission. You may decide to pay nothing or you may decide to pay any amount of money for admission. Moving forward to downtown. There are many buildings with stunning architecture.
Tampa Theatre is in 711 N. Franklin St, 7 minutes away from Tampa Museum of Art.
Downtown Tampa’s Sacred Heart Catholic Church should be on that list too. It was built in 1905. The predominantly 11th-century Romanesque granite and marble structure features a 135-ft dome and 70 stained glass windows.
You can walk 30 minutes to Historic Ybor City or you can take a bus (HART) to Centro Ybor. Ybor is a National Historic Landmark and is well known for its cigar industry, an industry that also brought many Italian, German, Jewish, Spanish, and Cuban immigrants. Spending a day in Ybor City is like going back in time, is to absorb a past culture. Katie, if you are hungry at this point and want to have a REAL Cuban sandwich you have to go to La Segunda Central Bakery. You don’t need more than a day to visit and explore Ybor. Ride the TECO Line Streetcar System (always free). This is the Ybor City’s streetcar. They make some stops from Ybor to downtown Tampa. Stop by The Florida Aquarium. Price for adults is about $34 which I think is a good price considering it's rated among the best aquariums in the US. The Florida Aquarium welcomes visitors to experience a wide variety of aquatic and terrestrial animals including sea turtles, sharks, lemurs, otters, etc. The average visitor spends approximately two hours here. I have in mind other awesome places that you can visit in Tampa Bay. Definitely needs two or three days to enjoy everything. John & Mable Ringling Museum of Art is the official state art museum of Florida, located in Sarasota, Florida. Mondays admission is free for the art museum. (Extra fees apply for the Ca' d'Zan home, Ringling Circus Museum and other tours). Recommend walking the grounds & gardens after you've finished seeing the art museum if not partaking in the extra upsale visitor items. The Dali Museum in St. Petersburg. Gallery Admission includes access to the permanent collection, special exhibitions, Café, Store and Avant-garden. $29 adults or $20 for students. I hope you can enjoy your visit!

Check out Armature Works - nice views & good eats there too!

University of South Florida is a nice area to explore, and they have the really nice USF Botanical Gardens.

Check out the Tampa Riverwalk, Sunken Gardens (St. Pete) or the St. Pete Pier™.

Walk Downtown Tampa, visit Channelside Drive. Visit Clearwater Beach.

If it's cold outside, it's easy to see manatees up close, south of Tampa in Apollo Beach (Florida).
Look for large outdoor art shows, most are free. They are popular in winter months.
The gulf coast beaches can be great, and free.
Walk the docks in Tarpon Springs.
Visit the St. Pete Pier™ - free.
Horse racing - cheap to get in.

I do believe our Tampa Museum of Art downtown is donation only on Fridays from 4-8pm. Tampa Riverwalk is super fun to walk at night or day and people watch. Walking through Hyde Park Village and grabbing a coffee and stopping at Goody Goody Burgers is also a lovely day. There are bikes all over that you can rent. If you like cheaper cocktails, Davis Islands main street is fun for that type of thing, one main street, very locals bar with mix of island folks and staff from hospital. I am unsure if you have the ability to drive out a bit but research Bok Tower Gardens, super cool. I would say walking Downtown, Bayshore Boulevard, Channelside Bay Plaza aka Sparkman Wharf and Hyde Park Village will pass you by our musuems and other stops and then you can sort of decide how you want to use the tight budget. University Of Tampa is also a pretty neat museum as it was a hotel. Have a blast, Tampa is a hidden gem with culture and art and vibrant folks. Oh! almost forgot my old neighborhood, for more of hipster vibe and I mean that kindly, check out Seminole Heights, old neighborhood and eats and Tampa Heights, Armature Works, which is technically at the end of the riverwalk. Again to be budget friendly for an experience if you are open, our oldest dive bar, The Hub Bar, you may sit next to a judge, attorney, homeless person, hipster or older retired person and they have the heaviest pour I have experienced in my life and travels and headed towards the big 50 :) Enjoy!

Take a walk down the Tampa Riverwalk, or drive/park and walk around Weedon Island, Florida. Saint Petersburg (Florida) downtown has a mural district, too! All free!