T-SQL How to Pivot on the Values of a Table?
Try this Query;

Select s.ItineraryID, R.ShortName as RoadTripName,  sum(EstimatedMiles) as TotalMiles, count(itineraryid) as TotalDays,
SUM(case DayType.DayTypeCode when 'XX' then 1 else 0 END ) as 'Planning/Prep',
SUM(case DayType.DayTypeCode when 'SE' then 1 else 0 END ) as 'Short Event',
SUM(case DayType.DayTypeCode when 'LE' then 1 else 0 END ) as 'Long Event',
SUM(case DayType.DayTypeCode when 'WD' then 1 else 0 END ) as 'Writing Day',
SUM(case DayType.DayTypeCode when 'TD' then 1 else 0 END ) as 'Tech Day',
SUM(case DayType.DayTypeCode when 'HD' then 1 else 0 END ) as 'Hiking Day',
SUM(case DayType.DayTypeCode when 'PD' then 1 else 0 END ) as 'Photography Day',
SUM(case DayType.DayTypeCode when 'LD' then 1 else 0 END ) as 'Layover Day' 
from  RoadTrip r inner join Itinerary s on r.roadtripid = s.roadtripid
  inner join DayType on s.DayTypeId = DayType.DayTypeId
group by s.ItineraryID,  R.ShortName 


Or another way using Pivot

Select ItineraryID, RoadTripName, EstimatedMiles,[XX] as 'Planning/Prep',[SE] as 'Short Event',[LE]  as 'Long Event',[WD] as 'Writing Day',[TD] as 'Tech Day',[HD] as 'Hiking Day',[PD] as 'Photography Day',[LD] as 'Layover Day' 
FROM 
(SELECT i.ItineraryID, r.RoadTripName,  dt.DayTypeCode, EstimatedMiles, 1 as daycount
    FROM RoadTrip r 
    inner join Itinerary i on r.roadtripid = i.roadtripid
     --Itinerary i 
    inner join DayType dt on dt.DayTypeId = i.DayTypeId
) ps
PIVOT
(
COUNT(dayCount)
FOR DayTypeCode IN ( [XX],[SE],[LE],[WD],[TD],[HD],[PD],[LD])
) as Pvt