I'm a practicing Roman Catholic, but considering attending a Greek Orthodox church instead of our local RC church. Will I be welcomed? I am Roman Catholic, but am considering attending an (Greek)Eastern Orthodox Church on Sundays instead of my local RC Church. Will I be able to receive communion? What differences should I expect? I understand that the Divine Liturgy is different from Catholic "mass", but as I read about the reasons for the split back in 1054 I have recently realized that I tend to lean toward the Orthodox beliefs.
I cannot speak for whether the Orthodox will welcome you or not, although I'm fairly sure they'll push for you to convert, that is, formally leave the Catholic Church and join the Orthodox one; depending on the Church, they might even not recognize your baptism as valid and thus require you to be baptized again, though most will allow conversion through chrismation.
Regarding the Catholic Church, however, Canon 844 forbids Catholic faithful to receive Eucharist from non-Catholic ministers except in emergencies:

Can.  844 §1. Catholic ministers administer the sacraments licitly to Catholic members of the Christian faithful alone, who likewise receive them licitly from Catholic ministers alone, without prejudice to the prescripts of §§2, 3, and 4 of this canon, and can. 861, §2.
§2. Whenever necessity requires it or true spiritual advantage suggests it, and provided that danger of error or of indifferentism is avoided, the Christian faithful for whom it is physically or morally impossible to approach a Catholic minister are permitted to receive the sacraments of penance, Eucharist, and anointing of the sick from non-Catholic ministers in whose Churches these sacraments are valid.
§3. Catholic ministers administer the sacraments of penance, Eucharist, and anointing of the sick licitly to members of Eastern Churches which do not have full communion with the Catholic Church if they seek such on their own accord and are properly disposed. This is also valid for members of other Churches which in the judgment of the Apostolic See are in the same condition in regard to the sacraments as these Eastern Churches.
§4. If the danger of death is present or if, in the judgment of the diocesan bishop or conference of bishops, some other grave necessity urges it, Catholic ministers administer these same sacraments licitly also to other Christians not having full communion with the Catholic Church, who cannot approach a minister of their own community and who seek such on their own accord, provided that they manifest Catholic faith in respect to these sacraments and are properly disposed.
§5. For the cases mentioned in §§2, 3, and 4, the diocesan bishop or conference of bishops is not to issue general norms except after consultation at least with the local competent authority of the interested non-Catholic Church or community.

So, if you're somewhere there are no Catholic priests, and you understand that it is better for you as a Catholic to receive the Eucharist from a Catholic priest (even if Eastern) rather than a non-Catholic one, you may go receive it from an Orthodox or Old Catholic or some other kind of non-Catholic priest with a valid Apostolic Succession and Eucharistic prayer.  It doesn't seem to be the case with you, though; so I would recommend looking for an Eastern Catholic parish near your home, where you may participate in Byzantine (or Antiochene, or Alexandrian) Divine Liturgy and remain in the Barque of Peter.
One more point, raised by AthanasiusOfAlex in the comments, is that Divine Liturgy at an Orthodox Church also does not fulfill Sunday obligation (save in the case of some very small Eastern Churches where the Church in question and her Orthodox sister have formally agreed to share priests).
The relevant Canon is 1248:

Can.  1248 §1. A person who assists at a Mass celebrated anywhere in a Catholic rite either on the feast day itself or in the evening of the preceding day satisfies the obligation of participating in the Mass.
§2. If participation in the eucharistic celebration becomes impossible because of the absence of a sacred minister or for another grave cause, it is strongly recommended that the faithful take part in a liturgy of the word if such a liturgy is celebrated in a parish church or other sacred place according to the prescripts of the diocesan bishop or that they devote themselves to prayer for a suitable time alone, as a family, or, as the occasion permits, in groups of families.

Again, all these issues do magically solve themselves if you manage to find an Eastern Rite parish somewhere you can attend; then you may attend Divine Liturgy there and never worry about violating any Canons, or worse, receiving Communion illicitly or invalidly.