Yes, the correct translation is "We look(ed) at the menu.". The problem with the verb "olhar" (look at) in portuguese is that you can use or not the preposition "para" and it won't change the meaning of the verb (at least, that's what I found on the web).
ex: A mulher, sentada na cama, olha para ele, mas ele não a olha. / A mulher, sentada na cama, olha-o, mas ele não olha para ela.
And I agree with it. On the other hand, if you pay more attention to this particular case, in portuguese, it does give me the impression of a deepest meaning (a very subtle difference):
ex: Nós olhamos o menu. - we take a look at/we check what's on the menu
ex: Nós olhamos para o menu. - we look directly to the menu
But again, you can see people using these two sentences to express the same thing and I think the sentence "We look at the menu.'', in english, can express those two meanings as well (?).
There are many verbs that when associated, or not, with specific prepositions will have a different meaning (in english: to look like / to look forward to / to look at / to look for / to look up ...).
It also depends on if the verb needs a preposition. This is called "Regência Verbal" in portuguese. I'm quite sure you already know it, but here are some links with lists of verbs that can assume two or more meanings:
http://www.blogdogramaticando.com/2011/04/regencia-verbal-completo-34-verbos.html (this one has funny pictures haha)
Well I asked him again with your responses. He says in practice, at least where he is from (São Paulo), it would be "weird" not to have the para except in a few specific cases such as maybe a command ("look at my daughter play piano") or the guarding sense I mentioned before (which he connects to a method of beggars 'guarding' a car as a way to force you to give them money). He has decided that it isn't particularly clear cut, and more or less agrees with Paulenrique's assessment. He isn't sure if other places in Brazil keep or drop it (and is now tired of me asking him about it :p) TL;DR: If you're speaking to someone from São Paulo, use the para or they'll look at you funny.
What does your friend make of the sentence "Nós olhamos os animais"? I was confidently saying in the discussion related to this sentence that it can mean "We look at the animals". As far as I can see Paulo agrees. See: http://dictionary.reverso.net/portuguese-english/olhar.
"501 Portuguese Verbs" book uses both with and without the "para" to mean to look at. The examples given are as follows: 1) Ela olhou para o mar - she looked at the sea. 2) Elas sempre olhavam todos que passavam - They always looked at all who passed by. Just by way of interest "olhe que" (present subjunctive/ imperative of olhar) means - "Don't forget that" ...taken from Linguaphone Curso de Portugues
This sentence has been bother me. I have seen it translated as: "look for" which would be more procurar and not olhar. "look at" which I think should be the more appropriate translation. "look to" which carries a connotation of expecting help I would like to hear what a Brazilian's take on this phrase "olhou para" would be.
My initial "The father looked at the daughter"was rejected , citing ""The Dad looked at the daughter" which is unusual English., and strictly incorrect as Dad = papai I thought. It also likes "the father looks at his daughter" , which assumes possession from the left field. I still think my first try is fine.