In Windows Phone Silverlight apps, you have the option of using a SQLCE database with the LINQ-to-SQL framework on top of it (see docs here). If you're considering building a universal app that will run on both Windows and Windows Phone, however, your only database option is SQLite (see here for more details).
That said - unless you need to perform queries across a large amount of structured data, a database is probably overkill for your app. You may want to consider simply using flat files (docs here) to start and only upgrading to a database if the amount of metadata for the diary entries grows beyond what you'd want to keep in memory.