Alternatively, hop on the Subway to Shoreside Vale, making sure you get on the 2nd door from the left. When you get to Shoreside Vale get off and you will glitch onto a ledge at the edge of the tunnel roof for some reason. Walk up the little slope in front of you, turn around and and do a running jump onto the tunnel roof.
NOTE: A part of the tunnel roof is not solid. This part is a few strides past the East end of the station- jump over it once you get to know exactly where it is. Use an M16 to manually shoot at the tunnel roof to see which parts are solid and which aren't. If you see sparks, the roof is solid, but if you see nothing then there is a hole here.
Walk along the tunnel roof towards the right [East] and go as far as you can until the tunnel disappears and it seems you are walking in mid-air. At this point you won't be able to see where the tunnel is, so will not know where to run, but just keep running straight ahead, and after a while you will fall off the tunnel roof into blue hell, before spawning on the little street in front of the airport in Shoreside Vale
This way you can't take a car with you, but it does mean you can get to Shoreside Vale without cheats. Then you can collect all the Hidden Packages to get the weapons at your hideout
To get back to Staunton Island, you need to get back into the Subway system. Unfortunately the entrance is blocked by a gate, so you will need to exploit another glitch. At the end of the little street in front of the airport are 2 billboards next to each other, almost parallel but at a slight angle to each other. Go around the back of these and run into the little gap between the billboards. You will sometimes end up on the street side of the billboards, but keep trying and you should fall into blue hell and spawn back on the street. If you run to the right as you go into the gap, you should land on the roof of the Subway tunnel as you fall through blue hell. From here you can run along the tunnel roof a bit and fall through the non-solid part of it into the tunnel itself. Now you can run or get the train back to Staunton Island.
Btw I'm not sure whether these glitches work on the PC version, but they certainly work on the PS2 version.