Visit the Paradesi Synagogue (check seasonal hours: often 10:00am–12:00pm & 4:00pm–6:00pm; confirm before you go) and browse spice/antique shops along Jew Town.
Home of the Nilgiri tahr—park usually open 7:30am–4:00pm (closed on some days/seasonal restrictions); excellent for short treks and views (book tickets ahead).
One of the best ways to spot elephants, deer and birds—boat cruises generally run twice daily (morning ~7:30–9:30 and afternoon ~2:00–4:00); buy tickets at the reserve office.