I'd recommend you to use Gower with subsequent hierarchical clustering. Hierarchical clustering remains most flexible and appropriate method in case of small number of objects (such as 64). If your categorical variable is nominal, Gower will internally recode it into dummy variables and base dice similarity (as part of Gower) on them. If your variable is ordinal, you should know that latest version on Gower coefficient can accomodate it, too.
As for numerous indices to determine the "best" number of clusters, most of them exist independently of this or that clustering algorithm. You need not to seek for clustering packages that necessarily incorporate such indices because the latter may exist as separate packages. You leave a range of cluster solutions after a clustering package and then compare those by an index from another package.
Similarly to the previous answers, most of the following answer of mine is not specific to SAS, as I use R. However, there is one exception to that - please see below. It seems that there exist substantial research efforts towards development of clustering algorithms for mixed data. More specifically, some algorithms were developed and/or adapted with a focus on categorical data.
In particular, some adaptations of traditional k-means clustering approach include k-modes, fuzzy k-modes, k-histograms and k-populations (for example, see this paper). Other solutions to the problem include hierarchical clustering, including ROCK, CACTUS and others. Probability-based clustering approaches for categorical data include already mentioned Two-Step cluster analysis procedure (seems to be SPSS-specific).
Recently some other streams of research, related to the topic, have appeared. They include using such approaches, as neural networks and genetic algorithms (for examples, comparisons and references, see this paper and this paper), information theory (for example, see this paper and this paper). An interest to the model-based clustering, specifically based on latent class analysis, is also growing (for example, see this paper and this paper - latent tree models - seems to be a mix of latent-based and hierarchical approaches).
Speaking of latent class analysis (LCA), finally, I would like to share the promised SAS-specific relevant information. This paper describes a LCA-based approach, called latent class clustering, and its implementation, using a free SAS add-in, which is available for download on this page.
Best Answer
This may come in late but try klaR (http://cran.r-project.org/web/packages/klaR/index.html)
It uses the non-hierarchical k-modes algorithm, which is based on simple matching as a distance function, so the distance δ between a variable m of two data points $x$ and $y$ is given by
$$ \delta(x_m,y_m) = \begin{cases} 1 & x_m \neq y_m,\\ 0 & \text{otherwise} \end{cases} $$
There is a flaw with the package, that is if two data points have the same distance to a cluster-center, the first in your data is chosen as opposed to a random point, but you can easily modify the bit in the code.
To accommodate for mixed-variable clustering, you will need to go into the code and modify the distance function to identify numeric and non-numeric modes and variables.