Create array of date pairs for next 10 days
Rather that continuing to append to arrive, just use the n offset from 'today'.

You can also use call strftime from a datetime object directly, like so:

def getNextTenDays():
    dates = []
    today = datetime.datetime.now()
    for n in range(1, 11):
        arrive = today + datetime.timedelta(days=n)
        next_day = today + datetime.timedelta(days=n+1)
        arrive_s = arrive.strftime('%m/%d/%Y')
        next_day_s = next_day.strftime('%m/%d/%Y')
        dates.append({'arrive': arrive_s, 'depart': next_day_s})
    return dates


If you are just going to return the strings, and throw away the actual date times you can do that in one go like so:

def getNextTenDays():
    dates = []
    today = datetime.datetime.now()
    for n in range(1, 11):
        dates.append({
            'arrive': (today + datetime.timedelta(days=n)).strftime('%m/%d/%Y'),
            'depart': (today + datetime.timedelta(days=n+1)).strftime('%m/%d/%Y'),
        })
    return dates


For here its a simple step to making it a list comprehension:

def getNextTenDays():
    today = datetime.datetime.now()
    return [
        {
            'arrive': (today + datetime.timedelta(days=n)).strftime('%m/%d/%Y'),
            'depart': (today + datetime.timedelta(days=n+1)).strftime('%m/%d/%Y'),
        }
        for n in range(1,11)
    ]