Access 2003 Report - want to show criteria dates

Only if you store them somewhere.
If you use a form to input your dates, rather than parameter prompts, then the report could get the dates from the form, assuming it was still open when the report ran.

How would I store them somewhere?

you can just use a variable to store the value of the criteria. that way you don't even need to redefine the query that drives the report, just filter the report with the criteria when you open it, eg below, replace names accordingly

 dim sWhere As String
    'set value of variable when you define your query

    sWhere =  " '" & me.txtboxDate & "' between [start date] and [end date] " 
'or you may need # depening on your pc settings
    sWhere =  "#" & me.txtboxDate & "'# between [start date] and [end date] " 

      'open report
    DoCmd.OpenReport "myReport", acViewPreview, , sWhere

where would I put this -
I have a macro that runs a query and then opens the report.
I need to run the query first because it is creating a new table that the report uses

avoid using macros, the simplest way would be vba code.
in the click event of whatever command button on your form, something like:
docmd.runsql "whatever sql syntax to create your table"

then execute the code i posted previously

Right now I have the report opening and in the report on the onopen event is the macro that first runs the query that creates the new table for the report. I am not using a form