I got a very odd request and I'm pretty sure the answer is 'no' already, but I thought I'd ask just in case.
Would it be possible to create a view that is sorted (maybe grouped as well I don't know) based on the last modified date of a certain field on the list?
*Note: No SharePoint Designer solutions or anything touching the code base (C#)
There isn't an OOTB way to sort on the last modified of a specific field of an item. You could easily create a view to sort and filter on last modified in general.
The closest OOTB way that I can think of would be to create a view based on general last modified and turn versioning on for the list. This way you can see what has been changed and go into the version history to see what was changed. This doesn't give you a nice clean view of only that field being changed, but I'm not sure what else your options are.
There is nothing in SharePoint to track the modification date of fields, you can track the modification date of item or the list itself, but for fields inside lists, it's not possible.
You could do so though by an event receiver, so you create your field that you want to filter by or group by using just a text field, and in your item updating method, check the values for these specific columns, and if any of them changed, update the value for that field to the value of the current time.
Update: I've just remembered you don't want to use custom code, but I'll keep the answer in case someone benefits from it.
The short answer is no, because SharePoint doesn't keep track of when each individual field is modified, just when the list item overall is modified.
That being said, you could implement this by adding another date field to the list called something like "Field X modified", and create the view based on that field instead of the OOB "Modified" field. That would, however, place the burden of keeping the "Field X modified" field current on the end users (meaning, they would have to remember that when they go in and modify "Field X", they also have to modify "Field X modified").
If you were able to use workflows, you might be able to make that automated via a workflow.
