There are several sources about connecting one’s tefilla to that of the tzibbur and the means of achieving that goal. Important sections of tefilla require a minyan, and it is more respectful to HaShem to join a group when turning to Him (the larger the better[2]). Additionally, davening with a group is more conducive to the tefilla being accepted favorably.[3]
The matter of davening at the same time that the tzibbur davens arises in the context of an exchange recorded in the gemara.[4] The gemara relates that Rav Nachman told Rav Yitzchak that he had been too weak to come to shul. Rav Yitzchak asked why he did not have someone tell him when the tzibbur was up to tefilla (apparently Shemoneh Esrei), as he would then have benefitted from the resulting eit ratzon[5] to help his tefillot. Tosafot[6] writes that there are different levels of advantage, depending on the type of connection with the tzibbur. When one davens together with the tzibbur, his tefillot are “heard”; when he davens at the same time but in a different place, they are “not pushed away.”
Of course, we do not understand exactly what HaShem’s “hearing” means, and there are also other factors that affect how HaShem views one’s tefilla. However, these sources give us some idea as to setting goals for proper tefilla, according to our circumstances.
In any event, scheduling one’s davening alone at the time of a minyan is not a full halachic requirement; it is a preference of which one should try to avail himself when he is not able to make it to a minyan.[7] It is similar in value to the opposite case – davening in a shul, but not at the same time as the minyan.[8]
Let us now address your question about determining what the time of tefilla is when there are multiple minyanim in one’s locale. The Semag[9] makes a comment that may shed some light on the matter. He says that if there is no local minyan, one should follow the time that “communities of Israel” daven. This implies that one should ideally follow the local minyan, but there could be some type of official average time. However, although we do not know the extent to which there was a uniform time for davening in the Semag’s day, we clearly cannot identify such a time nowadays. (Although there is a general preference for davening at the time of vatikin,[10] if the Semag had that in mind, he would have said so. This is certainly not the most common time.)
The Mishna Berura[11] seems to say that in places where there are many minyanim, starting from early in the morning, all times are acceptable. However, he and his source, the Chayei Adam,[12] are discussing refraining from davening before the right time (i.e., not too early), and they maintain that this issue does not apply when there are many minyanim. What should one do if he specifically wants to avail himself of the full positive element of davening at the same time as the tzibbur? Ishei Yisrael[13] claims that when there are multiple minyanim, all times are equally positive. Avnei Yashfeh[14] rules, based on an unidentified gadol, that in such a case, there is no preference (but he gives the impression that no time has a positive element).
We prefer the following compromise approach. Rav S.Z. Auerbach is quoted as arguing that the gemara’s implication of preferring davening at the time of a minyan requires that one focus on an individual minyan.[15] This claim works well with a position taken by his disciple, Rav Neuwirth,[16] that if one usually davens with a specific minyan but cannot join it on a certain day, he gets the positive element of davening when he davens at the time of that minyan, irrespective of when other minyanim in town daven. (This makes particular sense if this matter depends more on psychology than on mysticism.) Rav Neuwirth cites an interesting example from the Sha’ar HaTziyun:[17] If one is eating fleishig at seuda shlishit during the Nine Days (and therefore must finish eating by the end of Shabbat), he should stop when his regular shul has davened Ma’ariv. If one is not connected to a specific minyan and there are many minyanim in town, there is apparently neither any requirement nor any gain in trying to correspond to any individual minyan.