Yes, if you itemize deductions you may be able to deduct some of your mileage. You can't deduct commuting mileage, so your drive to the first location of the day--whether it is your office or a customer site--is not deductible. You also cannot deduct your mileage for the other half of your commute, that it, your ride from your last place of business (office or customer site) to your home. However, if you work at multiple sites, even if they are within your metropolitan area, you may deduct the mileage between those sites.
For example, suppose you spend your day in your metropolitan area, working at your office and visiting customers. You make the following trips:
Again, to deduct your business miles as an employee, you must itemize deductions (Schedule A). The miles won't be fully deductible because employee business expenses are part of the miscellaneous itemized deductions that are subject to the 2% rule.