Airport to Quito?

For Quito, Mariscal is safe enough if you are sensible (i.e. stick to the main streets, don't wander around drunk, take taxis at night), the same as you would need to do anywhere in Quito. It's certainly no more risky than the historic center, and probably significantly safer after dark. Robberies do happen, but they can happen anywhere in Quito. You are also far more likely to meet other people if you stay in Mariscal, reducing the need for you to walk around alone. Use common sense and be risk-averse and you should be fine.

Pifo is fine if you are just staying overnight prior to an early flight, but there's not much reason to base yourself there. You can take a bus into Quito (Rio Coca) it'll cost about $0.60 and take an hour or two depending on the traffic and road works. A taxi will be around $30 depending on how hard you haggle, and if you can find one willing to take you.

What's your budget for accommodation?

It depends if you want a night life while in Quito or just daytime activities. If you aren't that into partying I would opt for the colonial centre which is safe until 9-10pm as lots of people around and La Ronda which is quite active at night is super safe and taxis are cheap. The area around the Central Plaza is also very safe in the evenings as lots of people there and like La Ronda lots of security.. It seems more and more tourists are opting to stay in the old part of town which is definitely more interesting and picturesque.

We really liked the colonial center and it did seem safe in the early evening. We weren't out after about 10, but there were plenty of police everywhere. Lots of hotels and restaurants. Our interest was seeing the historical sights anyway. Just do not try to walk up to the statue on the hill, as you will very likely be mugged there.