Recommend me a tube integrated amplifier

Check out Decware.  They have a line of integrated amps from 2 watts up to 60 watt.  American made, well built, sound wonderful :)

This seems to be a nice system.  What price range are you looking at?  Of course Audio Note amplifiers will work well with their speakers.  I personally like the various iterations of the Soro and Oto.

I have have heard both AN-E and AN-K with amps from Synthesis Audio (Italian) and the combination sounds great.  Synthesis amps work well with a wide variety of speakers so I am not implying a special synergy here; they make great sounding amplifiers. 

The Roma 96 is a 25 watt EL 34 amp with a built in DAC that is no slouch.  It offers remote control of volume.  The A40 model (40 watt per channel KT-66 in pushpull) is further up their line and it is, to me, one of the great bargains in amplifiers; it delivers a big, authoritative sound that can compete with almost anything else out there.  The big brother A100 (also with KT-66, but more tubes to get to its 100 watt per channel rating) is very good too and will drive almost anything.  Both the A40 and A100 have terrific built in DACs and remote control of volume.  I own two flea-powered amps (about 5 watts per channel each) that have retail prices of about $50k and $100k, which I like a lot, but if I had to get rid of them, I could live with an A40 and not be missing out on that much.