It's more fun to ask the guards and other NPCs questions and find Chico yourself, but if you really want to know, here's his full routine.

He sleeps on a bed roll on Katla's farm from around 9pm to 6am.

Every day except Tuesday and Wednesday - Winking Skeever 6am to 9am for breakfast.

Every day except Friday - Winking Skeever 6pm to 9pm then he'll head to Katla's farm to sleep. If you see him on the way he should start singing and staggering like he's drunk.

If it rains or snows he'll take shelter in the Winking Skeever or he will stay inside his current location if he's inside when it starts raining or snowing.

Monday
9am to 11am - Temple
11am to 2pm - Sandbox outside the Bard's College
2pm to 4pm - Hall of the Dead 
4pm to 6pm - Fletcher 

Tuesday
6am to 12pm - Sandbox around Solitude docks, doing odd jobs like sweeping
12pm to 2pm - Blacksmith
2pm to 6pm - Bard's College

Wednesday
6am to 2pm Odd jobs at Katla's farm
2pm to 5pm Sawmill

Thursday
9am to 11am - Market
11am to 12pm - Pick flowers outside the college
12pm to 2pm - Bits & Pieces
2pm to 4pm - Radiant Raiment
4pm to 6pm - Angeline's Aromatics

Friday
9am to 2pm - Castle Dour
2pm to 6pm - Sandbox in the Blue Palace
6:15pm - 8:15pm (ish) - Does his comedy routine in front of the Yarl

Saturday
10am - 1pm - Busking in town square unless raining or snowing
1pm - 3pm - Fletcher
3pm - 5pm - Blacksmith

Sundays
10am - 12pm - Temple
12pm - 4pm - Bard's College