My husband and I travel frequently to see my parents and stay overnight with them and have found a couple of things work for us with our 3 year old. Especially when traveling, children are more likely to be anxious, sleep badly, eat less, and generally act out more in the unfamiliar environment. We definitely found the first night at a new place was very rough on all of us.
As such, a lot of the advice revolves around keeping things as similar as possible, and mitigating the other issues that can arise. If you can stay at similar places, or visit the same peoples houses (family members) that goes a long way to helping too.
Firstly, get them involved in preparations before you leave.
I generally let my daughter pick what clothes she wants to take and pack them. We talk about how in a few sleeps we're going to drive her to visit granny and grandpa and go in the car.
Secondly, take familiar things. Some favorite toys, books and her bedding. We had a camping cot we took with everywhere until she grew out of it. No matter where she slept, the cot and it's contents were familiar. Now we take a toddler mattress and her bedding. Even a nightlight to plug in.
Thirdly, take key moments to be family-only.
You've travelled far, the relatives are excited, granny is waiting, everyone is excited and overwhelmed, so stop and take a moment with just the nuclear family (whoever your child lives with) and take a break to settle in. Relax, show them where they will sleep, let them set out their toys, make sure they're comfortable, and just touch base and give them an opportunity to decompress. This is when you talk about how the drive went, feed them (see next point), change any diapers, deal with any behavior issues in private, and give them lots of hugs and attention. They need this time with just their primary cargiver(s) to properly relax and unwind.
Fourthly, pre-feed any young children before meals.
You can't rely on your child to eat when the adults do. The environment is new, the food may be different, they may be distracted by family members they haven't seen in a while, or overwhelmed by it all. Feed them something familiar, healthy and snack sized so that if they do end up skipping lunch or dinner they aren't hangry afterwards. They can eat if they want, but you'll be more relaxed too knowing they are fed.
Fifthly, prepare family/friends beforehand regarding potential behavior issues, and strategise beforehand. How will you handle a tantrum? Or hitting? I recommend using the same strategy at home (timeouts, etc) but in private, not around other people, and clue In family ("if she has a tantrum, we'll take her to our room to calm down", "if she hits you, say that makes you sad and you don't want to play anymore because you don't play with children who hit"). For me this is very similar between home and away, just in private.
Sixthly, for bedtime, exclude any relatives, stick to the routine, and give them space to fall asleep on their own if that's what they're accustomed to. My husband and I do family bedtime with no relatives, just us three, in exactly the same way as home. Bath, read books, tuck in, all the same at the same time. We take our time, talk about the day, have lots of cuddles and keep it as similar as possible. It is tempting to involve granny but that will stop your child from fully relaxing. When we are away she sleeps in the same room as us, but we take what we need from the room for the evening, and don't go in until we're ready, then we just quickly slip in to bed. We usually keep the door mostly closed but slightly ajar, and keep our voice levels lower. If she does come out, we calmly explain it's time for bed and take her back to bed. Some parents may choose to close the door, but that depends on the kid, if you have a monitor on them, if there's light in the room, how comfortable you are with that, etc.
I think the biggest key is to stick with the routine as much as possible, stick with the same behavior strategies as home (but in private) and spend lots of time just as a family to help them relax and be themselves. As much as relatives or friends are exciting, children will only be themselves and let themselves relax around their primary caregivers, and they need the privacy and opportunity to do that in order to not get too anxious and stressed.
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