Nested vs. 2-Way ANOVAs


I'm conducting analyses on my MSc data set, and am a little confused about how to think about my data in terms of statistical tests.

I have a series of data consisting of multiple dependent variables from 2 different sites. [Most of these dependent variables, though collected at each site, will not be compared together in the same tests since they're independent of each other and were collected randomly; for those that will need need to be compared together (such as a set of morphometrics taken from individuals), I'll be looking into multivariate stats.]
At each site, data were collected in a number of years (ex. site 1: 2007, '08, '09, '10; site 2: 1997, '98, '99).

I've been reading extensively about ANOVAs, since I want to compare the data between the 2 sites. However, I don't want any results to be confounded by the differences in years the data were collected.

I think that a 2-Way ANOVA is inappropriate, since each site was not sampled for the same number of years, nor in the same years.

Assuming the data meet the assumptions, can I perform a 1-way nested ANOVA with one dependent variable, such that the Main factor is Site (a fixed factor), and Year nested within Site (with year being a random factor)? Or would this be more suited to something else entirely?

Thanks for any suggestions you might be able to provide!