How can I open notepad as Admin only using Win + R window?
Solution 1:
Run Once as Admin
The command syntax you want to use is:
runas /user:<localmachinename>\administrator notepad
NOTE: Designating the machine name is optional. It works like this too:
runas /user:administrator notepad
Substitute administrator for the account name that has admin access. You will need to authenticate using this process.
As @EBGreen suggested in the comments, you can save the credential on the first execution and avoid reentering it on subsequent calls. This option only lasts for the existing logon session:
runas /user:administrator /savecred notepad
Reference:
http://technet.microsoft.com/en-us/library/cc771525.aspx
Always Run As Admin
You can also set it so that all programs run in admin mode. This is typically not recommended as UAC exists for a reason, but if you're so inclined follow the steps here:
Always Run as Administrator
Solution 2:
As far as I know, this task will be started with Admin rights if it is started using 
+R when UAC is disabled
Anyway, you can do the same if you press key, type notepad in the Search field and press Ctrl + Shift + Enter
Solution 3:
If you don't mind using a third party program, there are several programs named elevate.exe written by different people. These programs work (mostly) like this:
elevate.exe notepad.exe
and then a UAC dialog pops up. Confirm it and your notepad has admin privilege.
Here's a blog post about this: http://www.raymond.cc/blog/trigger-uac-elevation-from-command-line-with-elevate-utility/
Solution 4:
The runas method often suggested has a major problem - it requires the use of a different account (Administrator), with the associated different profile. Administrator also happens to default to disabled. Running as any other standard administrative account actually uses the UAC-restricted token, defeating the purpose.
It is possible to elevate as your current user purely through the command line without third-party tools, though it's a little more complicated. One way is through the PowerShell Start-Process commandlet. The full invocation is:
Start-Process -Verb "runas" notepad.exe
Shortening it, we can get:
start -verb runas notepad.exe
Running it from the command line, or from the Run dialog:
powershell -c start -verb runas notepad.exe
It's also possible to save a script that can be run simply as elevate, like in AgreeOrNot's answer - which, again, doesn't require any third-party tools.