Well you want to make sure everything is top shape. Did you have a survey done before purchase? If so then they likely gave you a list of things, normally listed as safety, urgent, and optional type levels of repair. If you did not have it professionally surveyed now would be a good time to do it. Most likely you will need one for insurance anyway. This will give you your repair list, but even great surveyors will miss things. So be sure to go over everything with a fine tooth comb. Keep in mind the engine will be critical, as deliveries are to get somewhere on a schedule, not a cruse. So you will likely have the engine on for both days straight.
Here is my basic list:
Engine, running perfect plus:
new fuel filters, and several (say 6 to 10) backups. (if fuel has been sitting in the tank it will likely get stirred up and any sludge will get picked up and clog filters.
compression tested (will give a basic idea of strength of the motor)
oil and filter change (might send old out for oil analysis to see if there are any major issues) Have lots of extra oil just in case it burns a lot, or leaks.
change transmission fluid
Rigging:
Check rigging for any signs of cracks in the swage fittings, replace any showing any defects. (be sure to check both lower and upper swages)
Check wire for any meat hooks replace any showing any defects. (be extra diligant of headstay wire if it has roller furling, and check again after test sails to make sure you don't have any wrapping of the furler)
Replace life lines if they are coated with plastic, unless you have receipts for them having been replaced in the past 3 or 4 years. Even if they look good.
Replace any running rigging that looks worn or stiff.
Electronics/navigation:
Make sure they all work and that you have charts (both electronic and paper) for your planed and surrounding areas.
Make sure the compass is accurately swung (hire a professional to adjust it if you don't know how)
Have at least two backups, so perhaps a chart plotter, a handheld gps and a tablet/laptop with charting software loaded and used.
Be sure to top up water tanks (soak with bleach and rinse well) and have a couple gallon jugs for each person each day for drinking. Don't expect the water tanks to be good enough for drinking till they have been cleaned and flushed several times.
Send sails out to be cleaned and any repairs done.
Have lots of snacks and food, full crew = happy crew.
Go out and sail several days well before departure (as in now) and make yourself very familiar with the rigging and controls of the boat. Know how to use all equipment on board including head and galley. nothing like a backed up head, or not being able to get the stove to light when you have sleepy crew that wants coffee.
Make sure you have updated safety equipment, and set up jack-lines and have harnesses available for all crew and good comfortable life jackets. Have extra fire extinguishers, and flairs, make sure you know where they are and alert all crew to there whereabouts. Have the local Coast Guard do a safety check, they will give you a sticker to put on your mast, and this often prevents boardings by them once you are out in the water.
If you can't do all of the above it may be better to arrange for the boat to be trucked or hire a professional.
Taking a new to you and unfamiliar boat into the open ocean is not something to be done lightly.
The recommendation of Sea Tow or Tow Boat US is a good one. Check to see who has the best coverage in the area you will be traveling.
What kind of boat is it?