Some countries have established refugee camps (e.g. Zaatari in Jordan) which puts financial pressure on host country to provide water, clothes, food and shelter to Syrian refugees
Host countries now house lots of orphaned children who have either had parents killed or separated from them due to the Syrian conflict. This poses as a problem for social services in Lebanon for example as they try and take care of these orphans
Some refugees have headed to urban areas which has put huge pressure on local health and education services
In Lebanon, some schools have started sending home Lebanese children at lunch so that they can teach the Syrian children in the afternoon. This has a detrimental effect on Lebanese nationals and literacy rates drop
Housing services in cities of receiving countries have been under pressure and house prices tripling as Syrian refugees increase the housing demand, even reports of Lebanese citizens being evicted from their homes
There is now a building of resentment between the nations and towards Syrians, especially as Syrians are seen to be costing Lebanese citizens jobs as Syrians are willing to work for much lower wages
Religious/ethnic tensions between locals and migrants (e.g. sunni and shia Muslim communities)
There is a fear that the conflict is "spilling over" into Lebanon and this is becoming apparent with suicide bombing happening (e.g. in Beirut 2015)
The only real benefits the receiving country have is that aid agencies (e.g. UNHCR) are bringing money into the area which could help improve the local economy