Come up with a per-diem charge per day for food and incidentals, add in the price of the accommodations you will require (YOU determine where you want to stay and its price), add direct costs of travel and then put a 10% addition on that.
I travel for business purposes pretty regularly and have for three decades. I refuse to quote flat-rate irrespective of location as WHERE matters a lot. Washington DC is an entirely different world than Paducah in terms of cost, particularly when it comes to hotels!
When someone calls and wants a price for a professional engagement I run the numbers on hard costs (actual travel expense including lodging), add my per-diem for food and incidentals, and then quote 110% of that figure. That's the number. My price for my professional services includes the time I spend away from the office end-to-end to begin with, so travel is exactly that -- travel.
It is VERY rare that I will entertain the client prepaying travel. There are exceptions -- I did a professional conference last year where I both knew the people and the location, and allowed them to book the room and flight on their dime while back-billing them after the conference for incidentals. I will only do that for clients I know both by personal experience and professional reputation -- "one offs" such as are the case for someone being hired to shoot a wedding get a flat travel quote and it is paid with the up-front deposit for the job, with my professional fee being paid in full at or before I arrive.