Erumbeeswarar Temple sits on a small hill at Thiruverumbur, east of central Trichy. It is an older, quieter Shiva temple than the city's headline sites, with a climb that gives views over the surrounding plain.
The temple is worthwhile if you have already seen the big three and want something less crowded. Its setting also gives a good sense of how sacred sites in Tamil Nadu often use even modest hills to command the landscape.