Don't use taxis. I've had terrible experiences, they ripped me off every time. Uber much better. Need data for that so I recommend Virgin mobile for cheapest data plan if you don't already have a local sim.
I've been walking a lot. I was never advised not to walk, just not to go alone out after dark. You see families with children out walking, so it can't be that bad. Just take the usual precautions: stay in busy areas, don't carry your original passport or loads of money or jewellery (though I often go out with my watch), be very aware of your surroundings.
I love carrera 7. My first escape from la candelaria was to get on kr 7 on a nice day with plenty of hours of daylight left and just walk down it until legs got tired just to see where it took me. (Then uber back.) Incidentally, it is also all pedestrianised for ciclovia (Sundays and public holidays when the main arteries are closed to motorised traffic until 2 pm) up to around calle 116 so it is possible to explore that way too.
If out on the bike after 2 pm and don't want to chance scary Bogota traffic, Uber offers an option called "uber bici" where your uber will show up with a bike rack!
Other flavours of uber that I've first encountered here are uber English (where the driver has passed a certain test of English proficiency), and uber Angel, which is where an uber driver shows up to drive you home in your own car if you've been out drinking and want to get home.
While I hesitate to say with my one month's experience that Bogotá isn't as dangerous as they say, I'd say it's OK to explore with caution.
Ciclovia map available here. In La Candelaria, bike rental is available on kr 3 #12-72 at Bogotá Bike Tours. They may prefer not to rent you a bike until after the bike tour has gone, however. Prices are reasonable, and they also offer great daily walking tours (maybe twice a day?)
There is a twice-daily graffiti (walking) tour from la plaza de periodistas near Las Aguas transmilenio station.
Museo de Oro is supposedly the best museum in Bogota (everyone raves about it). Free admission on Sundays, but only COP 3000 on other days anyway, with English tours at least twice daily (11 am and 4 pm, and sometimes maybe one at 2 pm or 2:30 pm, but that's not guaranteed, unlike the other two).
Museo de Bogota also highly recommended, but I have not yet had a chance to visit.
Best sushi I've found in South America was at Sushi Rail at Atlantis mall on Calle 81, in Zona Rosa.
Decent ramen at Tokyo Ramen on Carrera 11 and Calle 98, overlooking the little park.
Best time to randomly discover rodas is probably just before noon on a Sunday morning. Many groups will have training and/or rodas in parks including Parkway, Parque Nasional, and random street corners in Chapinero. These may be closed to outsiders, however, and only for group members.
I found a regular open roda in the pit right next to Museo Botero and opposite Biblioteca Luis Angel Arango on calle 11 and carrera 4. It's held fortnightly on Saturdays from around 4pm to around 5:30 or 6 pm. It's called the roda de tres and most people show up in street clothes.