Of course you can do this. In GA, just go to Audience >> Overview. Select the date range that you want. The unique visitors during this date range is listed below the chart in the box labeled "Unique Visitors".
In the Overview chart, you also select to see your data graphed hourly, daily, weekly, or monthly. On the left hand side, select "Unique Visitors" from the metric drop-down picker. That will give you your daily/weekly/monthly data.
Note that the daily unique visitors will not add up to the weekly or monthly unique visitors. If Joe visited on Tuesday and Wednesday, he will count as a unique visitor on each of those days. But he will only count once as a unique visitor for the weekly number.
My company's tool - Megalytic - lets you easily generate custom reports that can give you a lot of information about unique visitors - by country, landing page, referral source, social network, etc. You can get all this information by building custom reports in Google Analytics also, but we make it pretty and easy to share or print out as a PDF, and you can put as many custom reports on a single page as you want.