Galactic open clusters are since long recognized as one of the best tools for investigating the radial distribution of iron and other metals. We employed FLAMES at VLT to collect UVES spectra of bright giant stars in a large sample of open clusters, spanning a wide range of Galactocentric distances, ages, and metallicities. We present here the results for four clusters: Berkeley 20 and Berkeley 29, the two most distant clusters in the sample; Collinder 261, the oldest and the one with the minimum Galactocentric distance; Melotte 66. Equivalent width analysis was carried out using the spectral code MOOG and Kurucz model atmospheres to derive abundances of Fe, Al, Mg, Si, Ca, Ti, Cr, Ni, Ba; non-LTE Na abundances were derived by direct line-profile fitting. We obtain subsolar metallicities for the two anticenter clusters Be 20 ([Fe/H]=-0.30, rms=0.02) and Be 29 ([Fe/H]=-0.31, rms=0.03), and for Mel 66 ([Fe/H]=-0.33, rms=0.03), located in the third Galactic quadrant, while Cr 261, located toward the Galactic center, has higher metallicity ([Fe/H]=+0.13, rms=0.05 dex). The alpha-elements Si, Ca and Ti, and the Fe-peak elements Cr and Ni are in general close to solar; the s-process element Ba is enhanced. Non-LTE computations of Na abundances indicate solar scaled values, suggesting that the enhancement in Na previously determined in giants in open clusters could be due to neglected non-LTE effects. Our results support the presence of a steep negative slope of the Fe radial gradient up to about 10-11 kpc from the Galactic center, while in the outer disk the [Fe/H] distribution seems flat. All the elemental ratios measured are in very good agreement with those found for disk stars of similar metallicity and no trend with Galactocentric distance seems to be present.