Does anyone have any nursery recommendations? I'm looking for a variety of things: royal poinciana, hydrangea, birds of paradise, adondia palms, foxtail palms, etc. I am on a low budget so I'm trying to find the ones with fair prices.

Try Facebook marketplace, lots of the plants you mentioned at all different prices. Find lowest priced ones. Cheaper than nursery.

Those are all pretty common landscaping plants. Every nursery carries them. The big box stores to the little ones. Foxtails grow quick and easy, find seeds if really want to go cheap. Adondia, grow really slow but also easy from seed.

Rockledge gardens, a wide variety of plants, on US1
Their stuff has always survived and prospered for me.
or Craigslist farm and garden but you takes your chances...

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Tropical Island Nursery 560 S Plumosa St, Merritt Island, FL 32952

Its off the beaten path but has a lot of interesting plants and the prices are lower than most.
Great selection of Christmas trees also....

Thanks for the info all.