Anki stores all your decks in a single collection file, so there is no way to sync only part of a collection. However, there are several possible workarounds that may be useful:
Use two profiles. You can store the decks you do not want to sync in a separate profile (you can create and manage profiles by choosing File → Switch Profile). This is useful if you have a lot of media that you have no need for on your mobile device, or if you cannot place some data on AnkiWeb because of security or confidentiality issues. However, it has the disadvantage that you will have to switch profiles to review all of your decks, and you will not be able to get combined statistics easily.
If you decide to use two profiles, you can easily move data between them by exporting .apkg files with scheduling information and media.
Use subdecks. If your primary objection to syncing all of your decks is that you simply don't need some of them on the mobile device and don't want to clutter up the screen, you may choose to keep them in your collection and sync them, but keep them out of the way in a separate deck. One way to do this is to create a deck called
~ Desktop Only or something similar and drag all of your desktop-only decks underneath it (the tilde keeps it at the bottom of the deck list; you can use an underscore if you want it at the top or nothing if you want it to sort with the other decks). You can then keep this deck collapsed on your mobile device. While the information will still sync, you will not have to see it.