Depends on where you are.

How busy are the roads you want to ride on? Are there other bikers? What days/times do you want to ride at? Are there a lot of accidents or few relative to other cities? How comfortable are you on a bike?

Answering these and other questions for yourself can let you know how dangerous or not it is.

On average

Cycling is a safe activity. It's gotten a lot more dangerous due to lack of respect on the roads / culture war bullshit, but in absolute terms, cycling is still an extremely safe activity.

There are usually shortcuts through neighborhoods. Try to stay of the main roads. A stressful ride will wreck the experience for you, so take the time to find alternate routes that are more enjoyable and safer.

I would say, it depends on you mostly. How you’re riding, how much you follow traffic rules and pay attention. And I think, that you can ride almost anywhere and it would be fine, if you know what you’re doing and are confident enough. If you look at those crazy messengers on fixies, riding in NY on youtube. They’ve learned to be very aware of surroundings and they can predict what’s going to happen 3 steps ahead and they don’t even follow traffic rules at all, they seem fine. But of course accidents can happen to enyone.

What city?

As another person said, it depends.

Where I live (population under 175,000), many roads don't have bike lanes, but I only avoid a handful where the speeds are too fast and the roads are in poor condition.

Generally speaking, if you are visible, riding in a predictable way, and are aware of your surroundings, it should be quite doable.

Yeah, it depends on your locale. Never the less, one should always be as visible as possible. I always wear a neon green cycling jacket with red led/reflective ankle straps.

In your situation I would also get led lights for my bike. Two red ones for the back, and two white ones for the front so you look as much like a motor vehicle as possible; also, (perhaps most importantly) a mirror or two so you can see behind you.

Basically you would want to look like a motorbike.

It depends where the motorists are used to driving with bikes, and how fast they're going.