Like most people I only visited the Thanjavur temple called Brihadisvara Temple. The other ones aren't far but check this out: I took the train!! Yeah well, even I can be on a budget. Basically you go to the Trichy (that's Tiruchirappalli if you are a newbie), ask for the next train to Thanjavur which is often, pay the cheapo ticket price and ride 45min across the country.  The taxis wanted 2,500 for all this - ridiculous, unsure what the apps wanted though. The way back is the same. I asked for the time in advance and they even got me a reserved seat ticket. You can do all that on the apps if you want to so you know the times in advance. You can take a rickshaw or, like me, walk the 15min to the temple. The path is easy and only requires one tough-ish road crossing. Overall just from looking at pictures I think Brihadisvara is the best choice.

Brihadisvara Temple is the biggest of them too. You have to take off your shoes and socks to get in. It can get VERY hot and they don't do a good job covering the floor with mats well. That means after paying your small ticket fee for the storage you want to rapidly run to the shaded areas. That includes inside (only open after sunset) or the sides which has displays, people relaxing, people sleeping, people asking for money (no kidding). I had a lot of time to spend here so I took a long look at everything including the inside which I didn't know is closed until they told me but apparently the doors are still "open". You also can't take pictures inside. Anyhow, if you want to see the inside of the large temple you need to come at night.

My main time spent here was investigating the 81 of 108 dance karanas that are carved around the upper storey of the temple. It will take some time to check them all out. They are also described well in one of the nearby panels. It doesn't know why the remaining ones were left - probably because the owner, Chola king Rajaraja I, lost interest, or they couldn't find a good carver in time to replace the old one. Either way, you only get to see "most" of them but that's still very nice. 

Second interest is the design overall. It's architecture is brilliant. You walk through the large gate, see the temple in front of you, the walkways going around, smaller shrines nearby, a moat going around the outside - all well planned. Add to this the murals, inscriptions, the festivals they sometimes have, the carvings in the two mandapa, you'll be spending a long time here if you check it all out. I also mentioned the inside of the temple is only open at night which takes extra time. Perhaps the best viewing would be late afternoon and then stay for that opening.

Definitely worth seeing.