We went full time in a short bus so I had to give up a lot of my kitchen tools and appliances. But, I also modified my cooking because we can't carry the pantry we could have at home.
I kept a small hand mixer - the kind you can get for about $15 at the drug store - but it works great for whipped cream, mashed potatoes, and cakes. I'm not making enough quantity to need a stand mixer.
I kept a combo blender/food processor. It is smaller than standard but makes margaritas and milkshakes for two and can process enough food for a couple of meals.
I also kept a crock pot, though I did downsize to a 6-quart. I'm still getting used to smaller batches but it is easier to store.
And we kept the coffee grinder - good for grinding grain, spices, and coffee.
I no longer have a grill, breadmaker, deep fryer, etc. But I rarely miss them.
Most of the fancy appliances just take the place of something that used to be done by hand anyway.
We also eat and shop differently now, both due to space and availability of items. Currently we are in Florida and so have a wealth of fresh fruits, vegetables, and fish available. We only have a week or two of space in the pantry and so shop more often and are pickier about what we keep around. Rather than carry tarter sauce and cocktail sauce, I make my own and am considering making my own mayonnaise. You will also find that many food staples at home are hard if not impossible to find in other areas of the country. But you will gain access to new and interesting things to cook. The local grocery store here has almost no Asian food. I got into experimenting using Asian ingredients in the pacific northwest, where there was almost an entire aisle.
Just think of your traveling time as a food learning adventure. It is a lot of fun and really improves your ability to cook on the fly.
Best of luck to you!