* Μπορώ να παρκάρω εδώ; (Boró na parkáro edó;) This is a direct and generally understood translation. It's polite and suitable for most situations.
* Επιτρέπεται το παρκάρισμα εδώ; (Epitrépetei to parkárisma edó;) This translates to "Is parking allowed here?" It's more formal and suitable if you're unsure about regulations.
* Μπορώ να σταθμεύσω εδώ; (Boró na stathmévso edó;) This translates to "Can I park here?" using the more formal word for parking, "σταθμεύσω" (stathmévso). This is suitable for more formal situations.
For informal situations with a person, you might add a please:
* Παρακαλώ, μπορώ να παρκάρω εδώ; (Parakaló, boró na parkáro edó;) This adds "please" (parakaló) making it even more polite.
The first option, Μπορώ να παρκάρω εδώ; (Boró na parkáro edó;), is likely the most versatile and readily understood option for most situations.