Ternopil isn't on most tourists' must-visit lsts, and here are some suggestions of what you can do/see whilst you are here.
Lake Ternopil - actually a man-made reservoir, expanded and improved upon during the Soviet era when the local river was dammed. You can get a boat across and back for UAH10 (80p). There is a pretty walking area near Hotel Ternopil too. It is not the most exciting boat trip you will ever undertake, but it is nice to do on a hot day and will kill half an hour.
Near the lake and Hotel Ternopil is Ternopil Castle, don’t get your hopes up, it isn't the romantic 16th Century castle that originally stood here. It has been re-built since then (twice) and most recently in 1956 and it no longer looks particularly castle like. You can’t visit it as far as I am aware, and I am not sure exactly what it is used for.
Whilst in Ternopil I took lots of photos of churches and am not sure what all of them are now I am home! There are two that I went into and which stood out:
Church of the Resurrection (17th century) which was a small, charming church in the heart of the older part of the city. Interesting statues inside and a memorial to the 1931 famine outside.
Cathedral of the Immaculate Conception of the Blessed Virgin Mary (formerly the Dominican Church) is 18th century. Badly damaged during the Second World War, it was restored in the fifties and re-opened as an art gallery in 1959 but is now a church again. All the paintings inside were painted in the last 20 years, and the main one over the alter was finished in 2011.
Like many Ukrainian towns, Ternopil likes its statues and public art. One in Shevchenko Park is of the famous opera singer Solomiya Krushelnytska and there is another of controversial Ukrainian nationalist leader Stepan Bandera. Plenty more can be spotted in the park and its environs.
There are a number of museums in the town, which I did not get the opportunity to visit. These include regional art and history museums. I also understand that the town’s opera and ballet company produces a number of well-regarded productions in the local theatre, when at home (they were on tour during the summer, when I was there).