You’re free to register at any Catholic parish that is recognized by its diocese to be a Catholic parish. So, yes, you can register outside of your diocese if you wish.
That said, Catholics should be wary of the quasi-Protestant attitude of surveying “the market” and selecting a parish based on feeling “spiritually nourished” and “at home.” While the parishes in your diocese may have various problems – which is only to be expected, at least to some extent, because we’ll only find perfection in heaven – my guess is that those parishes offer valid sacraments. That means that you would be “spiritually nourished” at those parishes, as well as at your preferred parish, because Catholics are “spiritually nourished” through valid sacraments. As for feeling “at home,” that is simply a matter of attending a parish long enough to become involved in its communal life.
What will happen when the parish at which you want to register gets a new pastor, or a new liturgy committee, or a new this or that, and begins to disappoint you? Will you then seek out yet another parish? Or will you stick it out and participate in being part of the solution to whatever problem is affecting the parish?
While there is, unfortunately, just reasons to leave a parish that has become so problematic that one cannot worship in peace at that parish (see the articles linked below for more information), Catholics must be very cautious to avoid developing a “church-shopping” attitude as a routine solution to minor disappointments in parish life. It is possible that the Catholic who today shops for churches without just reason may become the radical Traditionalist or the Evangelical Protestant of tomorrow.
Problems In the Church by Jimmy Akin
Should I Stay Or Should I Go? by Jimmy Akin (Part 2, Part 3)