You can use either donde or dondequiera que for the meaning that you've expressed in your examples. Using one or the other doesn't depend on the verb that follows. The main difference in meaning is that dondequiera que emphasizes the total freedom of the choice of place, while donde makes it sound more like you're asking for a specific place. Although no translations are exact, this is basically the same difference as between English "wherever" and "where" respectively.
There's however another important difference. Dondequiera (que) is a long, high-sounding phrase, and it doesn't belong in the informal register of a conversation. It sounds bookish, even archaic, or like something you might hear in a romantic song. You shouldn't often encounter people who say things like
- Podemos comer dondequiera que gustes. ("We can eat wherever you like.")
- Adondequiera que iba me lo cruzaba. ("Wherever I went I ran into him.")
even though they're grammatical. They're OK for a story with the proper context, or a piece of poetry, and they might be more common in the spoken language in some places, but I'd counsel it's best to avoid them. Donde is enough.
One thing you can do, though, if you think you need to emphasize the total freedom of "wherever" in examples like the one you gave, is add some adverb like más or mejor to the verb expressing preference:
- Podemos ir donde más te guste. ("We can go wherever you like best.")
- Podemos ir donde mejor te parezca. ("We can go wherever you think best.")