Going around to different mosques in order to have more focus (khushoo’) in prayer

As far as I know, there is a difference of opinion concerning
the authenticity of this hadeeth. If we assume that it is sound, it may be
interpreted as meaning that this applies if doing that may lead to the
people abandoning the mosque that is closest to them. Otherwise it is well
known that the Sahaabah (may Allah be pleased with them) used to come to the
Prophet’s Mosque in order to pray behind the Prophet (blessings and peace of
Allah be upon him). In fact, Mu’aadh (may Allah be pleased with him) used to
pray ‘Isha’ with the Prophet (blessings and peace of Allah be upon him),
then he would go back to his people and lead them in prayer, even though it
was later. 

If a person frequents the mosque because of good recitation,
and because that good recitation of the imam helps him to focus in prayer,
there is nothing wrong with that. Otherwise, if there is the fear of any
problem resulting from that, or there is the fear that this may be regarded
as disrespect to the imam of the local mosque, if he (the person who goes to
another mosque) is a prominent figure and his going away from the local
mosque to another mosque may be regarded as undermining the position of the
imam, then in this case we say that he should pay attention to the potential
bad consequences of this action and avoid doing it. 

And Allah knows best.