I searched in the dictionary and found out that the verb "Loben" does not come in a reflexive form! So what does "mir" in this context belong to?
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The "mir" is kind of a reinforcement and changes the meaning from approval to strong approval. Also note that it's his town, not just the town, which gives even two times the relation to himself. It might be a matter of style too. – Trilarion Jan 25 '18 at 8:51
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You can use the reflexive form with any verb where the subject can also be the object. Reflexive forms are usually only explicitly mentioned in dictionaries when the meaning is different or when the reflexive form is mandatory. – RHa Jan 25 '18 at 9:23
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You searched in a dictionary ;) Duden gives two examples. – Carsten S Jan 25 '18 at 14:40
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1Wein auf Bier... – leftaroundabout Jan 25 '18 at 15:25
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1Wein auf Bier, das lob ich mir - Bier auf Wein, das lob ich mir! – Jo Mo Jan 25 '18 at 16:57
Two things to note here. First, reflexives can be added freely to verbs no matter what their verb frame definition says. The construction is typically something like this:
Komm mir nicht zu spät nach Hause!
= Don't you dare come home too late!
Second, Ich lobe mir etw. is an even more common idiomatic expression, meaning not that you literally utter praise, but that you thoroughly approve of something. (Dictionaries often fail to include all of these constructions because there's an awful lot of them, and it's hard to enumerate them when starting form the main verb only.)
... lob ich mir
Is often used as a fixed idiom to show respect/appreciation for something or someone. For example:
Du bist sehr gewissenhaft. Das lob' ich mir.
= You're very diligent. I respect that.
Also, dict.cc translates it to: My respect for...
But in the context of your question, i would translate it to something like
I appreciate my Leipzig
or maybe even
I'm proud of my Leipzig
