Hi! I live in Santa Barbara.
The Montecito Inn looks like it's actually in Montecito, not Santa Barbara? So if you are there, you are right on Coast Village Road, and it's a scenic little place with some nice restaurants. Depending on what you like, Los Arroyos (Mexican) I like, and Jeannine's Bakery is a great (but busy) breakfast/ brunch place.
As far as scenic drives go - here's what we do when people visit us (or what we did pre-kid):
One day visit: Go to the Courthouse and see the view from the tower. Go to the Mission and wander the Rose Garden.
Two day visit: Same day day 1, but also go to wine country. Generally that means driving the 154 up over the mountains. Sometimes we take a right at Camino Cielo and drive along until we hit the water tower - that gives a nice view of the city. There's a short hike called Knapp's Castle if you are into hiking (some of our younger friends are). It's basically the remains of an old mansion, but has great views of the backside.
I will second (or third) the Cold Spring Tavern.
Generally for the two-day visitors, once we get over the 154 (I hope nobody gets carsick?) we go wine tasting at a couple of places and then would have lunch in Solvang. We are partial to the Red Viking (not fancy food at all, but has a Danish buffet. My MIL is Danish, so it's a special Danish treat for us.) There are certainly nicer restaurants in Solvang. Then we would drive home along the ocean.
As far as walking tours of Santa Barbara go - along the beach is nice, and State Street has shops. The Funk Zone has wineries for tasting. There are a lot of panhandlers on State Street these days though. It got so bad a few years ago that I stopped going. I used to walk to the farmer's market with my kid(s) in the stroller every Saturday. If you are here on a Saturday, the farmer's market is nice. I've also heard good things about Santa Barbara Public Market, though I haven't been. (I have kids, I don't go places much.)
http://sbpublicmarket.com/For the beach, you can basically walk from Bird Refuge to Shoreline Park and back (it's 8 miles round trip).
Gardens...hm. I haven't been to Lotusland, and I haven't been to the botanical gardens since the fires several years ago. From your hotel, you could walk along the beach in Montecito, and there's some pretty foliage and flowers there too along channel drive.