To estimate the total cost of Marian's shopping trip, we can round each expense to the nearest whole number:
- Clothes: 56.17 can be rounded to 56.
- Books: 44.98 can be rounded to 45.
- Meal: 21.15 can be rounded to 21.
Now, sum the rounded amounts:
\[ 56 + 45 + 21 = 122 \]
Therefore, the best estimate of the total cost of Marian's shopping trip is $122.