Right on, well I'll do my best to suggest some places to visit. For places local to Santa Barbara, one is the Sunken Gardens (which I think is what you were referring to by the botanical gardens). The community college overlooks the harbor and from the overlook point, you can get a really cool shot of Shoreline Drive/E Cabrillo Blvd. There is Sterns Warf of course, but during the day, it is packed with tourists. The Zoo is pretty well known, but honestly, I've never been. The Santa Barbara Cemetery is pretty neat to see if you are just passing by. You can park along the road anywhere in the cemetery and walk around.
But my favorite place is Montecito. If I remember correctly, Sunday mornings (around 8 or 9) are car day. Along Coast Village Rd. you can see Mercedes SLS, Ferraris, Maseratis, ect. Last time I was there, I saw Katy Perry driving through in her Maserati. West Beach in SB is iconic, but Butterfly Beach is a bit less busy. It is across the street from the 4 seasons hotel and down the road from Ty Warner's home (which you can walk by on the Channel Dr. bike trail and check it out). If you go to Butterfly Beach, park and head down onto the sand. Then go east past the private club and find a sweet spot to lay out a towel and enjoy the coast. This part of the beach is not private, but mostly used by locals so it will not be busy.
For hiking and hot springs, my favorite is at the top of Hot Springs Road. You won't be able to park near the top, but find parking and start hiking up Hot Springs Road. You will pass some seriously expensive houses and your more likely to see a Bentley or Rolls Royce than an average car. When your getting near the end of the road and near the start of the hiking trail, you'll get the feeling like your walking towards someone's private driveway, but dont let that stop you. Eventually you will see the start of the trail. If you take the wide trail, it will take you to the Hot Springs. There will be signs saying stay away, but ignore them. The hot springs may not be set up or there will be people there, so you can continue on the trail to Saddle Rock. What a lookout from that view! If you are just going to head there, you can take a more direct, but steeper trail from the beginning. Also, I would recommend getting the route so you dont get lost, but you can take the same trail head to hike to Montecito Peak (I'm glad you like the picture!).
If you have time, the Channel Islands are definitely worth going! A good sunset picture can be taken at Father Serra Cross in North Ventura. If you do the very short hike by parking before the gate on Ferro Dr., you can stay there after sunset to avoid being locked in. And if you have a lot of time, the town of Ojai is neat.
I'm sure there is a bunch I am forgetting, but hopefully this info is useful. If you have any questions, feel free to ask!
