That is very close to your house shadow so sun exposure comes into play. What kind of sun exposure will it get as the sun goes over your house ( forgive me Copernicus ), full, partial or shade? Also, what type of soil and drainage will it have? This knowledge will help to give you an answer as to the type of tree that will be recommended by GOY members.

You could try the deciduous Kornus Kousa. It has lovely white blossoms - actually bracts not flowers - in early summer followed by small strawberry like fruits (inedible). It doesn't grow tall and is suitable for small gardens so it would probably suit your situation.

I think that 2 m is too close for any tree, a shrub would be more suitable for the situation. Avoid anything from the cherry family, they love to invade drains (but many trees will if they are short of water.

Had you thought of a dwarf lilac? Some are shrub shaped and some are trained as standards which will grow 4 - 6 feet tall depending on variety.

Acer in a pot. Camellia on a pot. Bay tree in a pot.
2m is very close and won't allow you to see a 'real' tree at its best.
depending on whether it's a sunny or sheltered spot you might consider training a fruit tree (on dwarf rootstock) against the house wall?

Where exactly are the drains and what sort of drains - 1 year old plastic is a different situation to 100 year old clay pipes.