I’m sorry, Terra, I didn’t finish answering your questions before posting my response earlier.
Things to do during the day...depends on what you’re into. Both venues have shopping. Downtown Miami has some great bargains in the small shops in the heart of downtown along Flagler Street which make outlet malls look expensive! Shopping in South Beach is trendy and expensive. If a day at the beach is your fancy, you’ll enjoy South Beach more. From Bayside Marketplace, you can take a boat tour of the homes of the rich and famous and other Miami sights, or a jaunt down to see Key Biscayne and the famous Stiltsville where home has stood on stilts for decades out in the middle of the bay. If you’d like to sip margarita poolside, be sure your hotel has a pool if booking a downtown hotel. You can sample the “day things” from anywhere - cabs are plentiful and things are fairly close, i.e. South Beach to downtown - just a 10 minute car ride.
Nightlife...hands down, South Beach definitely has a more intense and hopping nightlife - sometime too much!
Bayside has a live band at the Marketplace out next to the seawall in the marina every night. It can go as late at 11:00 p.m. or sometimes after midnight. There is also a Latin dance club there where folks salsa late into the night, but generally, the area closes up around midnight. Personally, I would not be wandering the streets of downtown/Bayside at night. I find Bayside Marketplace is quite safe, but keep in mind that when I go there, that’s where I go - and I don’t leave. We take our boat over and tie it up to the seawall, or hover in the water behind the band. For me, I prefer Bayside simply because I can take my boat over there.
As for safety issues, well, like any other big city, there is crime everywhere and Miami is not immune. Use common sense and you should be OK, but freak things can happen anywhere at any time. In South Beach, I’ve never felt threatened, but then again, I stick to the mainstream where the crowds are and don’t venture into dark alley ways (another reason not to drive a car - you won’t be forced to park on a dark side street somewhere).
Another place that is quite nice and also about a 10 to 15 minute ride from downtown is “The Grove” - Coconut Grove - a little more quiet than South Beach, but nicer than downtown. The Grove is more upscale and features “CocoWalk” which is a neighborhood of unique shops and great restaurants.