Thiruvanaikoil temple is in between two major roads Chennai (Madras)-Trichy by-pass road on East and Chennai (Madras)-Trichy GST (Grand Southern Trunk) road on west. Most of the buses from Chennai enters Trichy through the GST road, so you can get down just few yards before the temple at Thiruvanaikoil.
If you are coming on Train you can get down at Srirangam station and take route no.1 bus to Trichy junstion (or) Main guard gate and get down at Thiruvanaikoil bus stop (just 5 minutes from station). Almost all trains stops in Srirangam station.

If you want to come from Trichy Central bus stand, Railway Junction or Chinthamani (Chathram, Main guard gate bus stands) bus stand take domestic bus (Route No.1 mostly) to Srirangam. You can get down right near the Thiruvanaikoil temple's main street (Sanathi street), the temple is few yards away from the Thiruvanaikoil bus stand. You have frequent services for this route. Its a 30-45 minutes journey from Trichy Central bus stand / railway junction.

The best place to stay near by is Trichy City. You have simple, affordable descent hotels/lodges to star category hotels to stay near Trichy Central bus stand/railway junction for stay. Lot of restaurants are also close by from the hotels (most of the hotels have their own restaurants).

You can find small hotels near by the temple and in Srirangam. If you are looking for authentic restaurants you have either go to Main gurad gate (near Rockfort temple) or Trichy Central bus stand. You can find class restaurants and hotels there.