My website is gifting website so I need to let users select the date of delivery. I want that selection (textbox with calendar popup) on shipping details step. I can google for a free extension but I need to hear from someone who's already solved that issue. I also don't want to modify core files.
There are few extensions available like
A few additions to this based on my own experience:
Shatir's comment to the OPs question talk about kiril's solution here -> This module almost works on 188.8.131.52 but the date itself isn't displayed in the order in the backend. Rather than go through debugging this I just implemented this module;
Quick and easy, works fine and there are some backend config settings which made it useful. If I was doing it again I'd try this one (which I never found when googling);
As a footnote - The client originally bought the Mage-World Advanced Delivery Schedule module. Whilst I'm conscious of not wanting to bad-mouth specific development houses this module really does deserve to be bad-mouthed, that's all I'll say about it. Uninstalled and deleted.