ui-only field date format

Its really not that hard. You just need to select “override metadata” and select the “date” display type:

You can leave everything else blank. It will pull the date time data and express it without the time component. No Formula needed.

I also want to show the month and time in separate columns which seems I will need a formula.

The documentation seems it should look like MONTH(My_Date_Field__c)

What am i missing?

The key miss in your attempt:  Wrap field name in {{double braces}}  this is a data merge!

There are two formatting options for you.

Month Number:  MONTH({{My_Date_Field__c}})
Month Name:  FORMAT_DATE(“MM”,{{My_Date_Field__c }})

The “MM” format string comes from our Time Format syntax and allows you to format dates really any way you want.  Look for more information here: http://help.skuidify.com/m/11720/l/129505?data-resolve-url=true&data-manual-id=11720
Just know that your format code has to be wrapped in quotes - its a string that is passed into the formula.   

I’m trying to make a date field default to a value = to the first day of the month of two months from now. I’ve got a working UI-Only field that renders the text properly, e.g. my date field of 4/28/2016 makes my UI-Only formula field have a value of “6/1/2016”, but it’s just text. How do I get that value to push into a second date field and have it be read as a date?

Answer - You can have a formula field like that returns your adjusted date as text in the format YYYY-M-D and then pass that successfully to a date field and have it be read as a date. 

for my case, this formula looks like

YEAR({{CloseDate}}+31)+'-'+(MONTH({{CloseDate}})+2)+'-'+'1'