Try to visit in August when you should get a fantastic hotel deal in any of the hotels near the European Parliament (usually not sitting then).
You can enjoy the beautiful park nearby with its resident stork colonies or take a leisurely stroll along the river to the historic centre.
Another bonus of a summer visit is that there are free Son et Lumiere shows and street theatre at various riverside locations in the evenings.
For lunch,with the money you have saved on your hotel room,treat yourself to a special meal at one of the seriously good restaurants.
Or if you are like us and fail to read the small print, be embarrassed by only being able to afford starters and a bottle of wine in the evening.
The waiters didn't bat an eyelid and we were treated with exactly the same charm (and complimentary nibbles and aperitifs!) as the other diners.
Maybe we were lucky, but it did seem one of the friendliest, least stuffy 'significant cities' we have been lucky enough to visit.
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