Once you've figured out your ideal flight schedule, the next big consideration is price.
The days of cheap air travel are long gone, but there are still ways to find good deals. The further out from the travel date, the better - fares only go up the closer you get to travel. Sites like Priceline (which allows you to "name your own price") and Hotwire (which shows you a mysterious great deal with no details until you actually buy) aren't usually viable for touring, because you have to take whatever flight they give you, regardless of whether that fits into your plans. There are oft-quoted statistics that fares are usually best on Tuesdays; I haven't found a notable difference in my experience, but Your Mileage May Vary. Usually, fares are determined by how far in advance you're buying, what day of the week you are flying, the time of day, and the size of the airports involved in your routing (smaller airport = bigger fare).
As a touring band, your first stop should always be Southwest.com. They are the only airline left in America that will check 2 pieces of luggage per traveler for free, and their oversize/overweight charges for your keyboard or cello are the lowest around. They are also the only airline left that doesn't charge a penalty if you need to change your flight (but you will still be on the hook for any increase in fare). Plus, they know they have become the airline of choice for musicians, and generally treat them well. Depending on where you live you may not be able to score a non-stop flight, but the cost savings may make up for the timing risk.
(PRO TIP: Southwest's major drawback is their stupid cattle-call seating system. The extra $12.50 they charge each way for "early bird check-in" -- thus guaranteeing you a boarding spot in "Group A" -- will be the best $12.50 you'll ever spend. This is especially important if you're carrying on instruments, as it will ensure you'll find plenty of room in the overhead bins.)
If Southwest isn't viable, check out JetBlue next. They only give each traveler 1 free piece of luggage, and their oversize fees are a bit higher, but they are also very musician-friendly and treat checked instruments relatively nicely. Southwest and JetBlue tend to have comparable fares, especially more than a month ahead.
If JetBlue isn't an option either, then it's off to the major airlines.
Rule #1 if you're traveling with gear: don't fly United.
United really does break guitars.
And cellos, and banjos, and keyboards, and ...
It's crucial to factor in your projected luggage fees while comparing flights, because what appears to be a cheap fare on one airline might actually turn out to be more expensive once you've added in the luggage fees.
I should also add, since this just recently came up in conversation: Spirit Airlines is a no-go, despite their insanely low fares. The fare may look low, but then you will discover that you'll have to pay extra to actually sit down on the plane (which, since it's mandated by the FAA, is impossible to get around). And they charge as much for carry-ons as other airlines do for checked luggage. In the end, you will end up paying as much as (or more than) other airlines where you will have a much better experience overall. Save yourself the effort, and don't even bother looking into Spirit.
At The Airport
Once the big day arrives it's important to get to the airport early, especially if you're flying out of a big hub like JFK or O'Hare. Curbside check-in won't work if you've got large items, so you'll have to schlep everything inside to the ticket counter. Allow extra time for clueless ticket agents who don't know how to deal with musical instruments, or who try to saddle you with extra fees. (Asking for a supervisor will add a chunk of time to the check-in process.) Chances are you will have to bring your large items to security yourself, but this is a good thing, as you will be able to observe the TSA agents as they open up your instrument cases.
(PRO TIP: If you are checking stringed instruments, detune them before putting them in their cases! Baggage holds aren't pressurized, and I've personally witnessed impressive damage done to guitars and cellos that weren't detuned first.)
At security, if you are carrying any pedals, cables, small amps, or anything electronic with you, do yourself a favor and make it as easy for the TSA as possible. Take the electronics and cables out of your bag and put them into a bin, and make sure your amp is separate from your other luggage. Otherwise, you will lose valuable time waiting for the TSA agent to go through every little bit of your bag, after you've experienced the fun of the "Special Screening". (We've already claimed dibs on the band name "Female Assist", btw. Don't even think about it.)
If you will be carrying on your guitar, fiddle, mandolin, trumpet etc., your life is about to get a lot easier. Congress recently passed the "Federal Aviation Administration (FAA) Modernization and Reform Act of 2012", which includes a provision requiring airlines operating within the United States to allow musicians to carry on their instruments hassle-free for no extra charge, as long as they reasonably fit into the overhead bins. The major airlines have already started sporadically implementing this, but they all need to be in compliance on every flight by this coming February (2014), which is right around the corner.
Here is a great rundown of this law and what it means. That link also includes great tips on how to ensure you will board early enough to get some of that coveted bin space.
There you go. Sit back, relax, and enjoy not having to drive 20 hours to a gig for a change!