InstantUnicode is a “responsive script” for Indesign CS6-CC. Run the script once—to activate the listener—then go into your text and type the desired codepoint using the format uHHHH. For example, u0170 will be instantly changed into the character 'Ű'. Here is a quick demo:

As shown in the screencast, you can also deal with codepoints greater than U+FFFF. To do so, use the syntax UHHHHH (uppercase U), e.g. U1F4A1. InstantUnicode then inserts the corresponding character in your text, U+1F4A1 ELECTRIC LIGHT BULB, assuming your font supports it.

InstantUnicode is intended to run in InDesign CS6 and CC.
How to install the script in InDesign.
• This script can be installed in a “startup scripts” folder (in case you want to make it active by default.)

Bugs and feedback?
Please, let me know what you think about this script via Twitter.