If you're below level 30 then you can still get a helicopter for missions, but most of the usual places are empty. I used the helipad you can see on this map...
It's annoying to get a helicopter there, but you can do it. If you park up at the road and then survey the area with a decent mid-to-long range weapon then you'll probably see a helicopter, normally hovering above a helipad. Let the pilot land and then shoot him from where you are. This is the bit that's annoying. If you get too close then he'll take off and then he's gone for good.
If that does happen, or if there is no helicopter when you get there then just drive off and come back, in order to refresh the NPCs in the area.
Most of the time I've got a helicopter first time with this method, but sometimes I've driven off and come back again several times and had nothing.
As mentioned in CaulynDarr's answer, it's much easier to call MerryWeather and kill the pilot so I'd recommend that, but if you're below level 30 then you don't have that option.