… I'd've loved to post this as an official answer, but oh well.
For your first sentence:
« ce que tu penses » = what you think
« ce à quoi tu penses » = what you're thinking about / of
… I see the confusion. Are you trying to express the idea of “I'd really like to know what you think of my new costume”?
There are two structures in French, but the ideas they express are different, as you appear to have noticed.
« Ce que tu penses » comes from « penser [quelque chose] de [quelque chose d'autre] ». This structure is the one that carries evaluative overtones; it communicates the opinion or the judgement of someone with regards to something.
« Ce à quoi tu penses », on the other hand, is from « penser à [quelque chose] ». This one simply talks about the object of the thoughts of the person in question, or what they're thinking *about*.
You're asking for an opinion here, and not asking a general question about what's currently occupying the person's thoughts, so you should go with « ce que tu penses de ma nouvelle tenue. »
(By the way, the form of “please” here ought to be « s'il TE plaît ».)
For your second:
« Chez », no contest. The only way to interpret that is that you're ending up in their house (hence « chez des amis » = “at my friends’ place”) and spending the last bit of your holidays there. If you used « à » here you'd end up saying something weird that – to my near-native ears – vaguely sounds (if it's even grammatical!) like you were somehow ending your friends' own vacation (but that's another story).