Event with multiple days - multiple choices
The feature you're looking for is called price sets - in combination with the "multiple register participants" feature.


Set up the price set with Events menu » New Price Set.  See screenshot 1 below.
Once you save the price set, you'll new to create a price field.  Configure it similarly to screenshot 2 below.
If the annual meeting also has a cost, or there are other optional items, add those as additional price fields.
When configuring the event, on the Fees tab, change Price Set to the price set you just configured.  Note that this will replace your existing pricing, so make sure it's added to the price set.
On the event's Online Registration tab, check the Register multiple participants? checkbox.


That's it!  When someone registers for an event, they'll select how many people (see screenshot 3) and fill in the info for themselves (including payment info).  Then when they continue, they'll get a page for each of the next registrants where they can select individually (screenshot 4).  Screenshot 5 is my confirmation page, where you can see I've signed up three people with different options and collected all their names.