Invitations and announcements
Typically your destination nuptials will be smaller than a traditional at-home affair. Since this may be the case, when planning your at-home reception plan on sending more wedding invitations than announcements. Keep the reception small and light while you're away and have a big bash when you return. This may be the one occasion when you can combine the invitation and the announcement.
In some cases, if the actual ceremony is much earlier than the planned 'at home' reception, an announcement is sent separate from the wedding invitation. In this instance, you'd send an invitation to those who are coming to the destination, an announcement to everyone else and then another wedding reception invitation to those you'd like to have at the 'at home' reception.
Once you've decided what you're going to do for the reception, you should get those invitations in the mail. And make no mistake - this is not an everyday kind of party. You should treat this party as a real wedding reception, as that is what it is - just without the ceremony. You should have a cake that you and the groom cut, a first dance and even toasts. Take advantage of this opportunity to wear your wedding dress again, this is probably the only time you will get to re-wear your dress.
There is no rule that states that you can't have a reception after you've eloped. And there is also no rule that states that you have to have a reception. It's your big day and you can have it your way. If you do decide to have a reception after you've eloped, make sure your reception invitations state "we've eloped." From there you can treat your reception as any other bride would. You can still cut the cake and have the first dance if you wish. Again, this might be the one and only place you can wear your wedding dress again.
Just an announcement
Some couples choose to elope as a way to avoid the expense of the reception. This practice is perfectly acceptable as it is your party and you can do what you'd like. In this instance, make sure you send an announcement to all of your friends and family. And while they may want to celebrate with you, it may have to be done on a smaller scale.
This is your big day and you can make your plans any way you choose. Enjoy your romantic destination ceremony and reception and then come home and enjoy a great reception. And if you decide to elope you've got lots of great options for wedding invitations and announcements.