You won't regret going, for sure. Are you likely to go in peak Season or before/after ? Beach-wise it's very much a North-South split there depending on which direction the wind is coming from (it's relatively windy compared to Ibiza/Formentera so often makes much more of a difference). The really beautiful Southern beaches (which are far better than Ibiza and some more beautiful than Formentera) west of Cala Galdana are all accessed via spur-roads off a by-pass like hub around Ciutadella. It means you can't drive from one to the other without returning all the way to Ciutadella and then taking the next road off the 'spur'. Very strange, but it keeps the coastline much less impacted by development. Ciutadella is at the far-West of the island, whereas the airport and Mahon are in the East. Kind of like going to Portinatx from Ibiza Town before then accessing the South-West beaches - in other words, you really clock up the miles (and car-time) if you want to explore everywhere with a car.
I recommend you buy this book, which I picked up at Mahon airport one trip .. make sure you get it in English as it's published in a number of languages, but it's a very good overview and more comprehensive than most which are targeted at less adventurous travellers. Has a good overview map in the back too but not very large-scale (I bought a bigger one too). Once you get to grips with this book over the Winter you'll be wishing the Spring/Summer would hurry up and arrive so you can get on a plane as soon as you can and start exploring !!!!!
http://www.casadellibro.com/libro-t...ca-in-10-days-20-stages/9788484785057/2005952
This will give you some insights into the different faces of the island and just how diverse it is. You could spend days and days exploring and barely touch the surface - a bit like Ibiza really and it's not dissimilar in size. The Northern beaches like Pilar are all park and hike (a LONG way). Many of the Southern beaches are much closer to parking, but also more popular. A lot of nudity in the North, not so much in the South. Also bear in mind this is very much a "family island" so if you want more adult/isolated beaches they are more prevalent in the North way away from the access roads - but they are wilder and not "turquoise-blue-gleaming-sand" like in the South West.
Badia de Fornells is a must - definitely on a Kayak if you can, it's worth the effort. Menorca is kayak heaven - wind-permitting of course, unless you've been doing some serious workouts before heading out !! But it really is the best way to see much of the coast and so peaceful. You can also hire a bike/electric bike but the island is hilly so this isn't something to necessarily rely on if you're not confident with hill-climbing. Of course the Cami de Cavalls is an amazing construction - the path goes right around the island mainly on the coast, for hiking. Off this loads of other paths take you down to beaches and to other viewpoints etc.
Staying for a short trip it's probably best to focus on one area of the island on a first trip but if you go for 7-10 days you have time to see lots of it. Cova d'en Xoroi is in Cala en Porter which is quite near the airport off the road out to the West. It's not an island you can get round quickly/easily at night compared to Ibiza as a lot of the main road West-East across the centre of the island isn't dual-carriageway and has lots of radar. If you want to tap into any nightlife (such as it is) probably best to stay relatively nearby and not on the other side of the island. On an 8-day trip I'd actually split it between West & East hotel/apartment-wise.
Menorca is very proud of its nature conservation status and many areas feel very respected, something you really struggle with in Ibiza and Formentera now. Even finding a Quad-bike is a struggle as they are widely frowned on. Coming from Ibiza it's a bit like going to see your folks after a debauchery session ! But I don't mind as it means almost everyone you meet outside all-inclusive package hotel swimming pool environs has an appreciation of the natural side of life and an element of respect for it. Which is nice.
I'm sure Icey can chip in with some "must do's" from his explorations ... I'm more for encouraging people to read up and go seek out what attracts them, hopefully to find their own favourite new spots and come share them here

So much to see !