Estimating Azure costs for an asp.net website & Db?

Let me share my thoughts on this.

Before looking at costs, I think what you need to evaluate if a cloud platform is a right platform for your applications. The picture below summarizes some of the common application patterns:

2 biggest benefits (at least to me) that you get out of any cloud platform is elasticity and pay-per-use pricing model. Generally speaking for low volume sites, cloud is generally costlier than other hosting providers. The questions you may want to ask yourself are:

• Do my applications need elasticity as far as resource consumption is concerned? Or in other words, will there be a scenario where you would need 1 server for a week and then 10 servers for next week and then 1 server again week after that and things like that.
• Am I willing to pay some extra even if my resources are under utilized? Or in other words, will you be happy to host a site in a single VM even if with a hosting company you can host 10 sites in a similar sized VM?
• Will there be any scenarios where I have to handle predictable/unpredictable bursting in traffic?

If the answer is No to any of these questions, then IMHO Windows Azure may not be a right platform for you to host your applications.

There may be some components of Windows Azure which you can use - Storage for example where you don't have to worry about running out of disk space ever or Mobile Services so that you don't have to worry about building a backend for any mobile applications you may develop.