If I need a Blood sugar to be lower at 11am, what time should I make his basal rate higher?
If this is a "fasting" number, then yes, you can adjust your basal rate down to raise your fasting. You need to remember that insulin has a duration of 5 hours and will take 30-60 minutes to act, so reducing the basal at 10am will start to affect the blood sugar at 11am and the reduction will still be having an effect until 3pm. Sometimes it can be messy. You may fix 11am, only to find you now go high after lunch.
These sorts of question are probably answered better by our pumpers in the pumper forum.
Most say around 1.5 to 2 hrs for a basal change...so around 9:00am.
I also generally adjust at two hours before the time I want a change, so I would also adjust the basal at 9AM.