Quito, Ecuador and the Galapagos Islands

It's a great trip ahead of you. As for pickpockets, yes, they lurk in Quito and London, etc. While I never felt at undue risk, just use common sense with some suggestions on minimizing your risk of being a victim here: https://www.ricksteves.com/travel-tips/theft-scams. Seek current advice from knowledgeable local sources, such as hotel staff, as to places/times to avoid. Blockbuster attractions were not evident, but visiting the Iglesia de San Francisco and the Basilica del Voto Nacional were more than worthy. Just bounce around and soak up the general atmosphere, foods, etc.

We spent a week in Quito last month before going to the Galapagos. As for pickpockets, practice the usual precautions when you are in a crowded city. We found the people to be very friendly. We didn't have any unpleasant incidents.
Lonely Planet has a suggested self-guided tour of Old Town. Go early on a weekday and it should not be too crowded as the weekends. However, summer is peak North American school group tours. Our tour guide said that he had to wait to get into San Francisco church because there were 3 school groups ahead of him. I'm not big on old churches, so for me half a day in Old Town was more than sufficient.
If the weather is clear, go up the Teleferico. The ride and view at the top were fantastic. But take it easy, it's at 13,000' elevation. There is a senior discount. We did this in the morning (gets very busy on the weekends after 10:00 am) then grabbed a taxi to Old Town for lunch. Taxi was $4-5.
The Botanical Garden is very nice. Nearby is the Inaquito Mercado. This neighborhood, La Carolina, is a bit more upscale with lots of cafes and pastry shops. Do you already have your hotel booked? I prefer staying here instead of in Old Town. There are a couple of big malls where you can eat, get coffee, buy chocolates and/or ice cream.
Their coffee and chocolates are so good. We spent some $$ at the airport on chocolates to bring home.
Go to Mercado Artesanal in La Mariscal. The area is a little bit sleazy with lots of bars, but you can get some really great, inexpensive stuff in the Mercado. It closes at 6:00 pm. We went at 4:00 on a Sunday and it was not crowded. However, the sun goes down around 6:00. We left before it got dark. Didn't feel comfortable walking in that neighborhood after dark.
Arrange a tour guide to take you to Cotapaxi or Mitad del Mundo?
Take a day trip to Mindo to the cloud forest, cacao farm and chocolate making?
You can PM me if you have any questions.

My visit was 4 years ago, but then the biggest concern was the bus for pickpockets. They are jammed so you wouldn't notice whether the person bumping you is picking pockets or just the crowdedness. My solution was to walk. I don't carry a back pack, so I think that also reduces temptation. If you take daytrips by local bus (say Otavalo), don't leave any purse, bag, etc on the floor. Keep it on your lap. Distance buses are notorious for theft from floor bags.
Hop on, hop off bus. I liked the museum with the pre-columbian art, but I don't seemit on the map. It was near Parque el Ejido, but must have moved. I enjoyed poking around the casa museums in Old Town.
It is hilly, so the HOHO bus is a good option to reduce wear and tear. I stayed two different apartments. One was in Old Town, the other was up a steep hill. I should have twigged when I was sold on the view of the city below. One has to go up to get those views😔

The museum of pre-Columbian art is in Old Town, Museo Casa del Alabado. The house is one of the original 1500's houses per our tour guide. Yes, it is worth a visit.
Don't take the public buses. Taxis are cheap enough. If you do a day trip, tour guides are around $60-80. Worth it.
We took the bus once. Coming from Boston, I know how to push my way out off a crowded bus. But my husband who is from LA doesn't have a clue on how to ride public transportation. My friends and I got off. He got stuck inside because people were pushing to come on. The doors closed and off he went.

Michelle, yes, the Old Town museum but also another, maybe ethnological museum in a large 'modern' building at the far end of the park I mentioned. There was a great local eatery below for a cafeteria type menu del dia. I think it is now the Mindalae Ethnological Museum in a new location.

We just returned from Quito this morning. While you should always pay attention to your surroundings, I did not feel unsafe in Quito. I used the same precautions that I would use in any major U.S. city. I did not wear a money belt or neck wallet. The ONLY thing I did was buy a tiny carabiner clip to hold my zippers together on my purse.

As far as what to see in Quito, what do you like most? History? Art? Food?

I agree with prior advice to take the precautions you would in a large city - keep your wits about you, don't offer the opportunity for theft. Personally I wore a money belt. Since you only have two days, I'd focus on the old town center and hire a guide or driver to take you to the equator and go to Intinan museum. Chocolate is better priced a the grocery stores - depending on where you stay there is likely a Supermaxi near by). The elevation will be noticeable to you coming from Galapagos so take a taxi or Uber. I used Uber multiple times and had a good experience - cashless (set up ahead of time, use a credit card likely to be accepted like Visa or MC, not AMEX) and efficient.

We took the usual precautions and I have a number of hidden, zipped pockets in my backpack. Cameras were clipped into the backpack too. Since the busses were so crowded, we paid for taxis to go places in the side. For day trips, we hired a driver through the hotel. We followed the advice of hotel staff and avoided places they said to avoid. We visited all the major churches, San Augustin, La Compania, Santo Domingo, San Francisco, Basilica, Plaza de Independencia, El Panecillo, and of course the funicular (teleferico). We also went to Quicentro mall and the museum. Outside of town we visited Otavalo, Ibarra, La Mitad del mundo, and the equator monument that’s not on the equator. There were a couple other small towns we visited, but I don’t recall their names. We never felt unsafe walking around, but stayed away from the historic center after dark.