The weather stays pretty darn near perfect here. However, if it's winter or early spring, check the forecast for rain! San Francisco gets about a month's worth of rainy days in those seasons. Take a historic tram around the city and do some sightseeing or stroll down the famous Market Street which offers plenty of dog-friendly restaurants and shop for you to visit on your daily outing.
The environment of South Beach is a 50/50 split between natural and artificial. Inside the city blocks, commercial and residential areas pretty much consume the landscape. However, towards the Bay, it really opens up into beautiful, wide-open spaces with sea breezes and ocean views. Head out to the end of a pier, enjoy the ocean air, and look back on the city for a moment of peace. Make sure to schedule in some greenway time in case your doggo needs to go!
The best dog park in this area is definitely Rincon Hill Dog Park. It has enclosed, off-leash areas and grassy patches with places to sit and watch your pup play. Do note that the playground is in close proximity and keep it on your radar if you're working with a dog with sensitivities to small children.
Further north along the Bay, you also have the option of visiting Rincon Park. This spot isn't an off-leash location but it hosts beautiful views of the beach and city. Meanwhile, located at Harrison and Freemont, Emerald Park is a small little oasis of nature in the middle of the metropolitan area. It's semi-enclosed and has shaded benches.
Lastly, on the south side of I-80 is South Park. South Park is an oval-shaped getaway that was opened in 1852. It sits between Bryant and Brennan Street and there is tons of seating, grassy landscaping, and cool architectural structures you can climb, sit on, or relax under.