Ask anyone what there is to do for free in Brevard and you get "go to the beach." True, but incomplete. This is the list I'd actually give someone who just moved here, including the honest caveat on a couple of things that get marketed as free and are not.
Watch a rocket launch, for free
You do not need a ticket to watch a launch. Space View Park at 8 Broad St in Titusville is a free public riverfront park, open dawn to dusk with free parking, and it looks straight across the Indian River Lagoon at the Kennedy Space Center pads about 15 miles out. Sand Point Park, 101 N Washington Ave in Titusville, is the quieter alternative locals use when Space View gets crowded, same free waterfront setup near the Max Brewer Causeway, plus a splash pad for kids while you wait.
What is not free: Playalinda Beach inside Canaveral National Seashore has the closest views of any public spot, but it is a National Park Service site and charges a $25-per-vehicle entrance fee (free if you already hold an America the Beautiful annual pass). The gate closes 30 minutes before a launch and fills up fast. Jetty Park at Port Canaveral also charges a parking fee, and depending on which pad is launching, a berm can block part of your view. Go in knowing which one you are actually paying for.
Walk a real nature trail
Erna Nixon Park, 1200 Evans Rd in Melbourne, is a free 53-acre preserve of old Florida hammock with a roughly 3,000-foot boardwalk and a nature center, open daily 9am to 5pm, with free guided tours most weekends. Turkey Creek Sanctuary, 1518 Port Malabar Blvd NE in Palm Bay, runs a 1.85-mile boardwalk where manatees, gators, and otters are commonly visible right from the walkway, open 7am to sunset, no admission. Both are the kind of spot people drive past for years without knowing they are free and open to anyone.
Brevard's Environmentally Endangered Lands (EEL) Program maintains roughly 75 miles of trails across the county, all free to walk. The Enchanted Forest Sanctuary in Titusville, 470 acres with educational displays, is the flagship site if you want to start with one.
The bioluminescence question, answered honestly
The Indian River Lagoon really does glow at night in season, roughly late May through early October, strongest around new moons. But every actual way to see it is a paid guided kayak tour, generally $50 to $85 a person, because you need to be out on dark water away from shore lighting for it to show. I could not find a free public shore-viewing spot for it, and I am not going to pretend one exists. If you want to see it, budget for a tour.
Farmers markets, worth the free browse
The Eau Gallie Farmers Market runs the 2nd and 4th Saturday of the month, 10am to 2pm, at Eau Gallie Square Park in Melbourne. The Cocoa Village Farmers Market runs every Sunday, 10am to 2pm, on Riveredge Blvd in historic Cocoa Village. Browsing costs nothing either way, and both are a good read on what's actually growing and selling locally right now.
Hours, fees, and seasonal schedules change. I have sourced everything above to an official page where one exists, and flagged the two spots that are not actually free. Verify the exact date and time before you drive out for a launch specifically, they slip constantly.