It's a global flood. There are several logical points why.
First, the gathering of all of the animals in the world would be useless, if the Flood was only a local flood. If the Flood was only local, not all of the animals would drown, and thus, bringing all the animals of the World on the ark would have been a useless act.
Secondly, if the Flood was only local, would all the people die? Obviously not. There'd be other people in the world that wouldn't have died besides Noah.
Thirdly, if the Flood was only local, why did Noah have to spend 100 years to build a massive ark, when all he had to do, was merely pack his bags and walk to some other place on Earth? Consequently, why build a massive 400 ft. Ark, if it's only a local flood?
Lastly if the Flood was local then did God break his promise not to Flood the world again? Hasn’t the Mesopotamian Valley been flooded many times since Noah?
Now, the major problem that you posed, was that , where did all the water go?
Edit:, Due to Caleb's statement, I looked it up, and found this:
Even if the glaciers and ice caps melted, the oceans would only rise some 70 m (230 ft), yet Mt Everest rises 8,848m (29,029 ft) above sea level.
It may surprise you to learn that we don’t need any more water to cover the earth. There is already enough.
The reason water doesn’t envelop the globe now is that the earth’s surface is uneven. The ocean basins sit low and the continents sit high. Some mountains are especially high and some ocean trenches are very deep, but these extremes do not account for a large percentage of the earth’s surface (see graph).
If the earth’s surface were even, then there is enough water in the oceans to cover the globe to a depth of about 3 km.
This suggests that, during the Flood, the ocean floor moved vertically relative to the continents, something mentioned in the Bible (Psalm 104:8 NASB).
In the first half, the pre-Flood ocean basins rose and the pre-Flood continents eroded down until water covered everything.
That does not mean the earth’s surface would have to be completely even. The ocean basins would have only had to rise enough for the water to cover everything.
Then, in the second half of the Flood, other parts of the earth’s crust sank. The water flowed off our continents into new ocean basins. Movement of the earth’s crust at this time also pushed up new mountain ranges, including the one that is home to Mt Everest.1
So where did all the water go? It is in the ocean.
Just for the reader, Psalm 104 : 6-8 states:
Thou coveredst it with the deep as [with] a garment: the waters stood above the mountains.
7 At thy rebuke they fled; at the voice of thy thunder they hasted away.
8 They go up by the mountains; they go down by the valleys unto the place which thou hast founded for them.