Downtown is very safe; obviously be smart with your surroundings but you'll be fine. Don't hang out near the Hard Rock Cafe unless you like being surrounded by tourists. Take the monorail (it's free) to Brickell and enjoy drinks and dinner there; it's only a 5 minute monorail ride from where HRC is. If it's past midnight on a weekday/2-3am on a weekend, go to Park West (also in downtown) for drinks, as all the drink spots there are either open into the early morning or simply don't close. Or take in Uber into the arts district for trendy bars/restaurants ($6-8 ride from downtown, if even).

You don't need to to rent a sunbed, just bring a beach towel and pull up a spot. Your belongings will most likely be safe. I've never worried about leaving them with my towel. But, again, be smart about it (e.g. bring a wallet with one credit card, little cash; don't leave a fancy watch). The best part of the beach is South Beach between 5th and 17th.

Miami is a late city - dinner time is 9/10pm, bars are open until 4-5am even on weekdays - so keep that in mind when planning your day. If you like shopping, hit up Lincoln Road (traditional retailers like H&M, Diesel, etc.) or Design District (high-end like Cartier, Louis, etc.).

Within downtown get around using the MetroMover for free, otherwise use Uber, which is incredibly cheap in Miami.