I have a Tier 2 General UK visa which is valid until 2019. Can I travel to Ireland (Dublin, Belfast) without an Irish visa? It would be for a short holiday.
You can travel anywhere within the Commont Travel Area (including Ireland), but you must bring your proof of valid leave in the UK with you or you will be 'removed' at the border which can leave a blemish on your immigration record.
You need a visa to enter the Republic of Ireland unless you are in a visa exempt nationality.
As a general rule UK visas and leave to enter or remain in the UK are not valid for Ireland as it's a different country. Certain holders of UK visas qualify for a visa waiver but that's limited to certain nationalities, and according to the Irish immigration authorities only applies to short-stay UK visas.
You could take a trip to Northern Ireland on you visa as this does not involve leaving the UK.