Determinate K in K-Means Clustering
Wang, Kaijun, Baijie Wang, and Liuqing Peng. &quot;CVAP: Validation for cluster analyses.&quot; Data Science Journal 0 (2009): 0904220071.:

To measure the quality of clustering results, there are two kinds of
validity indices: external indices and internal indices.
An external
index is a measure of agreement between two partitions where the first
partition is the a priori known clustering structure, and the second
results from the clustering procedure (Dudoit et al., 2002).
Internal
indices are used to measure the goodness of a clustering structure
without external information (Tseng et al., 2005).
For external indices, we evaluate the results of a clustering algorithm based on a known cluster structure of a data set (or cluster labels).
For internal indices, we evaluate the results using quantities and features inherent in the data set. The optimal number of clusters is usually determined based on an internal validity index.

(Dudoit et al., 2002): Dudoit, S. &amp; Fridlyand, J. (2002) A prediction-based resampling method for estimating the number of clusters in a dataset. Genome Biology, 3(7): 0036.1-21.
(Tseng et al., 2005): Thalamuthu, A, Mukhopadhyay, I, Zheng, X, &amp; Tseng, G. C. (2006) Evaluation and comparison of gene clustering methods in microarray analysis. Bioinformatics, 22(19):2405-12.

In your case, you need some internal indices since you have no a priori clustering structure. There exist tens of internal indices, like:

Silhouette index (implementation in MATLAB)
Davies-Bouldin
Calinski-Harabasz
Dunn index (implementation in MATLAB)
R-squared index
Hubert-Levin (C-index)
Krzanowski-Lai index
Hartigan index
Root-mean-square standard deviation (RMSSTD) index
Semi-partial R-squared (SPR) index
Distance between two clusters (CD) index
weighted inter-intra index
Homogeneity index
Separation index

Each of them have pros and cons, but at least they'll give you a more formal basis for your comparison. The MATLAB toolbox CVAP might be handy as it contains many internal validity indices.

More information:

Determining the number of clusters in a data set
How to determine which method is the most reasonable clustering results?
How can I detect if my dataset is clustered or unclustered (i.e. forming one single cluster)?
How can we choose a &quot;good&quot; K for K-means clustering?
Cluster analysis in R: determine the optimal number of clusters