Hi Hecti,
I don't know the timeshare that you're staying at however I have been to Ibiza several times and love the place.
There are two distinct parts to Ibiza, one is the legendary nightlife and party atmosphere and the other is the laid back, relaxing side.
St Eulalia is regarded as the quieter side of the island and is favoured more by families and older people. It is relatively close to the the capital, Ibiza Town, which is the more historic and 'upmarket' part of the island.
Travelling west you then reach the resort of Playa Den Bossa. This is popular with families and those with young children and has better beaches than Ibiza Town which is more of a port. If you look at a map of Ibiza on google maps you can gauge some idea of distance as it takes about 20 minutes to walk from Playa Den Bossa to Ibiza Town.
The airport is close to Playa Den Bossa and is a relatively cheap taxi ride away. I would suggest that a taxi would be reasonable to Santa Eulalia however renting a car would be a good idea. That way you can explore the island more easily.
San Antonia is the other major tourist district on the island however this has gained a notorious reputation for being full of drunk, violent louts. Unfortunately this reputation is true and I hated the place. It is cheap, tacky and full of 18 to 25 year old idiots, mostly British and Irish, who can't handle their drink. Avoid it like the plague except for one evening in order to remind yourself how awful it is and never to book a hotel or apartment anywhere near there.
I've never been to the northern side of the Island so I can't comment on what it is like.
The clubs on the island are fantastic although expensive and it deserves the reputation as the party capital of Europe.