Accidentally deleted the Downloads folder, a windows "Special Folder", how to restore?

Windows keeps track of the location of special folders in the registry. Have you ever used regedit.exe? Start that program and browse to:

Computer\HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\Shell Folders

In that folder, there is an entry with this name:

{374DE290-123F-4565-9164-39C4925E467B}

That entry should be set to the location of your Downloads folder, usually:

C:\Users\[username]\Downloads

There is another entry here:

Computer\HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\User Shell Folders

Same name as before:

{374DE290-123F-4565-9164-39C4925E467B}

This entry should be set to:

%USERPROFILE%\Downloads

I am not sure what you mean by "right clicking does not show the 'Location' tab", but here is the contents of the desktop.ini file from my Downloads folder, check to see if your desktop.ini is the same... maybe it will help. I am running W7X64.

[.ShellClassInfo]
LocalizedResourceName=@%SystemRoot%\system32\shell32.dll,-21798
IconResource=%SystemRoot%\system32\imageres.dll,-184

I came here searching to resolve the corresponding problem "unavailable/messed-up Downloads folder" in Windows 10.

The top-voted answer from William Jackson almost completely solved my problem, but there is 1 more step to do in Windows 10 (Home):

In Win10, if you open "This PC" in Explorer, additional folders are shown above the section "Devices and drives" and one of these folders is the one related to "Downloads".

If this folder doesn't behave as expected, start regedit.exe and go to the folder:

Computer\HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\User Shell Folders

In this folder, the following entry specifies the target of the additional folder beneath "This PC" in Explorer:

{7D83EE9B-2244-4E70-B1F5-5393042AF1E4}

The usual value for this entry is:

%USERPROFILE%\Downloads

In my case, I had to change the value from %USERPROFILE%\Desktop to %USERPROFILE%\Downloads to restore the original behavior.

If this entry is missing, I guess adding it will bring back the additional "Downloads" folder beneath "This PC" in Explorer.

For the changes to take effect, at least log out from your Windows session and log in again.