County Offaly (Contae Uíbh Fhailí) is in the East Coast and Midlands region of Ireland, and traditionally part of the province of Leinster. It's mostly lowland and rural.
The county is named for the ancient Kingdom of Uí Failghe which covered much of it. The Normans divided Ireland into shires or counties, but they were repulsed from the midlands to shelter behind the palisades (the "Pale") of Leinster. The Tudors resumed the land-grab, swept aside the old Irish kingdoms, and in 1556 renamed this area "King's County". That king was Philip II of Spain, married to Queen Mary of England: but she died childless, one of the great "what-ifs" of British history. And King's County it officially remains to this day. All sorts of royal names were replaced at Irish independence (Kingstown to Dún Laoghaire, Queenstown to Cobh, and so on); but it's some measure of Offaly's importance that the legislators clean forgot to change this one.
Offaly has the Slieve Bloom Mountains along its southeast boundary but is mostly lowland. Many areas are bog - notably the Bog of Allen - while to the west it's bounded by the flood-prone River Shannon. Agriculture and peat-extraction are traditional occupations. Yet this was no rustic backwater: Tullamore was the unlikely scene of the world's first aviation disaster in 1785. In the 19th century, the Grand Canal stimulated trade. Birr had the world's first automobile fatality in 1869, and its "Leviathan" telescope put it at the leading edge of astronomy for 70 years. The railway arrived in the 1850s and industry developed along it, but the big growth came when motorways put Offaly within commuting range of Dublin. In 2016 the population was 77,961.
Visit Offaly is the county tourist agency.
Dublin Airport (IATA: DUB) is the obvious choice by air, as it has a good range of flights at competitive prices, and good onward transport.
Trains run from Dublin Heuston via Kildare and Portarlington to Clara and Tullamore, with five or six daily. They continue west to Athlone then branch either to Athenry and Galway or to Roscommon, Castlebar and Westport.
Trains from Dublin Heuston towards Cork stop at Ballybrophy, which has a branch line service to Roscrea, Nenagh and Limerick.
There are direct buses from Dublin to Edenderry, Tullamore, Birr and Banagher.
Bus 73 traverses the country twice a day from Waterford via Thomastown, Kilkenny, Carlow, Stradbally and Portlaoise to Tullamore, Clara and Athlone.
The Grand Canal starts from Dublin and is navigable throughout; it crosses the county via Edenderry and Tullamore to Shannon Harbour near Banagher. The Shannon forms the western boundary of County Offaly and is likewise navigable throughout from Limerick up to Athlone and Carrick-on-Shannon, with onward canals to Enniskillen, Drumshanbo and Boyle. The Grand Canal is connected to the Barrow Navigation, which runs to Athy, Carlow, New Ross and Waterford. Dublin is also linked to the Shannon by the Royal Canal, but that passes further north near Longford.
Public transport is confined to the corridors described above. The must-see monastic site of Clonmacnoise has no public transport. So you need wheels: the distances are not great and it's not hilly so a bike would do.
There's car hire in Tullamore, but you'll do better to hire from the airport.
If you're in Dublin without a car (and you positively don't want one in the city) then consider joining a day-tour: Bus Éireann is one reliable operator.
The Rock of Cashel in County Tipperary, Brú Na Bóinne in County Meath and Lough Owel in County Westmeath are all about an hour's drive from County Offaly.