North Central Sri Lanka : Polonnaruwa
Polonnaruwa is a city in the North Central Province of Sri Lanka. The second most ancient of Sri Lanka's kingdoms, Polonnaruwa was first declared the capital city by King Vijayabahu I in the 11th century AD and maintained its status until the 13th century. In 1982 the ancient city of Polonnaruwa was inscribed on the UNESCO World Heritage List. The history of Polonnaruwa is available at this link 
What's nice about Polonnaruwa is that the ruins are in one compact area so you can visit them quite easily. Just one three wheeler ride from where you're staying to the entrance and you can walk about them all day long.
Polonnaruwa is 216 km or 134 miles from Colombo.
To travel there, you've got several options. They are, in order of preference, car, train and bus.
Car is the easiest. Any taxi service (+94 11 2556 556 or +94 11 2818 818 are two numbers of cab companies you can call) will charge you around LKR 30 per km (approx LKR 13,000 roundtrip) (as of mid 2007). Make sure you ask for a Nissan Sunny or Toyota Corolla or you might be sent a crappy car. Advantage is that you will sit in air conditioned luxury all the way to Polonnaruwa and the road is quite nice with plenty of greenery along the way. The old, massive trees tend to shade into the road once you leave the urban areas, creating a canopy effect. Trip is five to six hours inclusive of breaks for food, fruit and shopping (although shopping along the way is just overpriced and not recommended).
Train is next, though frankly, bus is kind of tied with it. It's quite cheap: you'll that find the three wheeler ride to the train station costs about as much. You get on the train to Trincomalee at Colombo Fort station (http://www.srilankatourism.org/lang/en/traveller/trainschedule.php), connect in Gal Oya and you're in Polonnaruwa. The trip'll take you a good part of a day and the train leaves the station at 6.15am so plan accordingly. It is not however an air conditioned experience but it is a train with all the scenery and Theroux-like (http://en.wikipedia.org/wiki/The_Great_Railway_Bazaar) hijinks that implies.
Bus is always my third option. Buses also leave from Colombo Fort but from a slightly different location. Take the intercity to Polonnaruwa. With luck and blessings from whatever deity you subscribe to, you should arrive in Polonnaruwa in six to eight hours.
Bicycles are the best way to get around. Most guest houses will rent out bikes, but be sure of the condition when you pick it up. Check if the tyres are properly inflated etc.
Just north of present-day Polonnaruwa town, 140km (90 miles) north of Kandy, are the ruins of ancient Polonnaruwa, which date from the late 10th century, when the Chola kings of southern India invaded Sri Lanka and conquered Anuradhapura.
Entrance fee is 3000 LKR (or 25 USD) as of March 2012. Unfortunately, the round trip tickets for the cultural triangle (50 USD) are no longer available.
In this area, you can find plenty of wild life reserves. Try to find a reliable person and visit the places like "Minneriya", "Kawudulla"
Avoid eating from places where they sell the food in open markets. Do not go to places where you see nice hoarding out and stingy inside. Food hygiene is very important. If it is too hot, there is a greater chance that the food is not safe.
There're dozens of guesthouses, mostly situated along Batticaloa road. price negociable if staying longer. usually starts from LKR 800, with WI-FI atleast LKR 1000.