Do you have all of the maintenance records for this vehicle’s 200k miles?
Whether you do or not, the first thing to do is to make sure that EVERYTHING is up to date with its maintenance.
Take out the mfr’s maintenance schedule (it could be contained w/in the Owner’s Manual, or it could be in a separate booklet), and make sure that everything listed for the 120k, 150k, and 180k mileage intervals has been performed. If you don’t have past maintenance records, then–unfortunately–you have to assume that none of the required maintenance has been done.
Pay particular attention to an entry in the maintenance schedule for timing belt replacement. I don’t recall if your engine has a timing belt, or if it uses a timing chain, but if it has a timing belt, that part (along with the belt tensioners & the water pump) needs to be replaced every 8 years or 105k miles (whichever comes first). If it isn’t replaced on schedule–in your case, by 210k miles–you risk truly catastrophic engine damage when that belt snaps.
Even if bringing maintenance up to date doesn’t help with the hesitation symptoms, up-to-date maintenance will make it easier to diagnose the problem, and it will help to ensure that you can add a lot more miles over the next few years without a breakdown.
Regarding maintenance, one or two items have been deleted from mfr’s maintenance schedules over the past few years, in an attempt to make their cars look virtually maintenance-free. However, these deletions do not change the reality that changing transmission fluid (& filter) every 3 years/30k miles is essential. And, it is also very important to check/adjust valve lash. Both of these items no longer appear in most mfr’s maintenance schedules, even though they are still vital.
So, in addition to the procedures listed in the mfr’s maintenance schedule, I urge you to include transmission service and valve lash service to the list that you give your mechanic. For the symptoms that you mentioned, it would probably also be a good idea to have him clean the Mass Air Flow sensor (MAF) and the throttle body.
Do NOT go to a chain-run establishment for the maintenance. Find a well-reputed independent mechanic in your area. Ask friends, neighbors, and co-workers for recommended mechanic’s shops.
Please let us know if you have further questions!