Hey there. I lived in Morocco for 3 years–2 years in the High Atlas mountains and another year in Fes. I’d be happy to help you out, though with the caveat that a lot has changed in the many years since I was there (as in, they have internet now).
If you are staying only in Marrakech, Mt. Toubkil is nearby–highest mtn in morocco and in north africa. It’s over 13,000′, so is an adventure trek if you feel up for it.
If you plan to move around at all, definitely go to Fez. It is one of the five royal cities and is absolutely amazing. The medina (old city) is probably the best in Morocco.
Not much to see in Casablanca, except the Hassan II mosque. Be aware than non-muslims are not allowed to enter mosques in Morocco (the prohibition is a cultural, not a religious, prohibition)–this mosque is the only exception, and it is exquisite.
If you head south to Zagora or another desert location and see those blue scarves that the nomads wear…know that they’re not color fast. If you wrap it around your head without washing, your skin will turn blue.
If you go vegetable shopping, don’t ask for ‘zucchini’–ask for courgette (the french word). ‘Zucchini’ is a bit too close to a vulgarity in arabic.
Do NOT spend time in Tangier. It is terrible. So many folks come over on the ferry from spain just to ‘get a taste’ of morocco that it is the worst harassment I ever experienced in the whole country. Tangier is not morocco—don’t be turned off by it.
I believe you said you’re going in May/June 2013, so you will not be there during Ramadan (muslim month of fasting). For anyone who is there during Ramadan (mid July-mid Aug 2012—it moves about 2 weeks earlier each year) be aware that *even in major cities* you will be very hard pressed to find any food shops or restaurants open during the day (fasting is dawn to dusk).
Two fun facts–Morocco was the first country to recognize US independence back in 1776, and Marrakech was the first-abort site for a space shuttle launched from Cape Canaveral (if it failed to go into orbit).