Oh dear, you really have been handed an unpleasant task there, you have my sympathies!
The first thing to realise is that you won't be able to please everyone, with such a large diverse group as you describe there really isn't going to be something that pleases everyone so you are going to have to aim for the something that will appeal to as many as possible. Some won't like the activity you prepare and some just plain won't like doing company activities (I know I fit into the latter category, I can't stand the things!).
Your question doesn't provide any detail as to the parameters you've been given so these points are pretty general and might not all apply:
Have the activity take place during working hours
This is often a sticking point for the company since they lose productivity during the time spent on the activity but people are generally more inclined to do something company-related when it doesn't impact on their free time. Also even those who aren't massively enthused at the particularly activity will often prefer it to working so that reduces that barrier to buy in. Something that extends after hours in a purely optional manner isn't quite as restrictive but if it requires them to stay late then it will cause problems for many in terms of their outside lives - picking kids up from school etc.
Ensure it doesn't cost the employees anything
The amount of companies that expect their staff to pay out of their own pockets for company activities is something that continually surprises me. It's rubbish and people hate it! Remember when considering this aspect that even if the company is covering the cost of the activity itself there maybe ancillary costs (transport, childcare etc) that can end up falling on the employees so be aware of this.
It's a cliche but in many cultures (particularly western such as the US, UK, Europe etc) alcohol is a social lubricant and the phrase "Free bar" is practically a magic spell. Not to everyone of course but it sure can win a lot of fans.
Ask the staff what they want
Depending on whether you already have some ideas you could put a shortlist out to a vote, or if you are completely stumped you could ask for suggestions and take the one that has the most votes while remaining feasible.
Organise something with a friendly but competitive element and offer prizes that the staff would want, this can be anything from "real" prizes such as vouchers/gift cards etc to extra vacation days.
Don't make it "mandatory"
While this might up the actual attendance figures in the long run it's utterly counterproductive. Even people who would quite like to take part could easily end up resenting being compelled to attend.