I went there for work a few years back, and spent two weeks in Bangalore a few years later to. I'll write up this post assuming you haven't been to India before, so sorry if I'm wrong and telling you stuff you already know. Also, please tell me you already have a visa. I have a horror story about getting mine, but it was a 5-year business visa which may be different from what you need.
Definitely visit a temple or two - one of my favorite Indian souvenirs is a copy of the Bhagavad Gita in the local dialect that I got at a temple in Bangalore (In Bangalore it's Kannada and in Coimbatore it's Tamil, not Hindi, btw). I didn't go to a temple in Coimbatore itself but I'm sure any of the bigger ones will have a good gift shop.
My absolute favorite part of the Coimbatore trip was a side trip to Ooty. You should definitely go there for one of your open weekends. It's a gorgeous resort town way up in the Niligiri Mountains, about 85 km (52 miles) outside of Coimbatore. In January, this meant that the temperature was about 30 degrees cooler than it was in the city. I have lots of pics.
We took a charter bus, and including the one pit stop we made, it took 5 hours to get there. I cannot overstate how much the combo of bad roads and traffic will slow you down, but if you're in a car it might go faster. The drive is beautiful, though:
If you stop somewhere along the way, do not leave any windows open when you get out of your car - at this rest stop, I watched an enterprising monkey climb into a parked car and steal a bag of Cheetos. And speaking of rest stops, ask your driver to stop somewhere that has a "Western toilet" - a regular Indian toilet is usually just a hole, like an outhouse. Bring your own tissues in case there's no toilet paper and definitely bring your own hand sanitizer.
The other stop we made on the way there was at this woman's coconut stand. It was set up a ways out of the city on a quieter part of the road. She'll cut the top off of a fresh coconut and carve out the meat (which you can eat if you want) and then stick a straw in it so you can drink the fresh coconut milk. This was the one time I didn't follow the guidelines to not eat cold/fresh food that hadn't been heated, and I have no regrets. Didn't have any stomach issues and the coconut tasted amazing.
Here you can see a tea field in the back of the photo. The tea from Ooty is known for being some of the best in the country.
One day we walked about 3 km down this road from our hotel to a tea shop and had masala chai. They served it in these little metal cups that stung your fingers at first, till the tea cooled a bit, but it was delicious.
A few other random things and tips for India travel in general.
Coimbatore itself is pretty conservative compared to bigger places like Bangalore, but I'm assuming you're a guy so this may not be something that affects you - the social standards for women there are much different than for men. You won't see any women drinking alcohol in public in Coimbatore, for example. And don't expect there to be alcohol at social gatherings. I wasn't expecting this but the Europeans I was with had prepared and brought their own booze. One night, after a big company meeting, we all hung out at this one guy's hotel room and were joined by our male Indian coworkers. Several of whom had brought weed. But none of the Indian women ever hung out with us after hours.
Definitely try to do some shopping at the Coimbatore mall, and pick up some pashminas for the women in your life. Or for yourself, if that's how you roll. They're super expensive by Indian terms but not so much by American/European terms. I have two hand-woven cashmere pashminas that cost about $60 each. They had a really cool weaving exhibit when we were there and you could watch them make a pashmina right there.
My Indian coworkers would not let us women go anywhere by ourselves in the mall. As a guy you should be fine; just keep an eye out for pickpockets and whatnot.
You will need to take your shoes off to go inside a temple. There will likely be a little old lady at the entrance who'll take your shoes; be sure to have some cash to tip her with when you pick your shoes up as you leave.
Many tourist attractions have different entry costs for India citizens vs non-citizens. They're not checking passports or anything - if you aren't visibly Indian you'll pay the bigger fee.
Also, many of the tourist attractions have rules about taking pics inside. Sometimes they aren't allowed at all, and sometimes you have to pay an additional fee for the privilege. I made the mistake of taking an unsanctioned photo inside the sultan's palace in Mysore and was quickly corrected by a large, armed Indian man who worked there.
I don't know if this happens to guys too, but my coworker and I (both very pale white girls) were asked countless times to be in photos at various tourist attractions. Sometimes it was with one or two people, and sometimes with whole families. I don't know if it was because we are white, or girls, or both.
Hope this helps! If I think of anything else, I'll post. Overall, it'll be a great trip. I'd love to go back to India for non-work purposes and take my family.