In most CFA analyses, the chi sq value will not reach p>.05, especially if you have a large N. Most people look for CMIN, i.e., chisq/df, of <3, or the change in chi sq between nested models, i.e., two models with a minor change in structure, the chi sq for this being (diff in chisq) with (diff in df) df.
The Modification Indices suggest links to change in your structure. Do this incrementally, checking the change in chi sq after each one, to see if it has really helped. You should only make changes that are theoretically sensible, in terms of your model. Start with the largest sensible modofication.
The MIs with the =~ operator are most use, as these are between latent (endogenous) and observed (exogenous) variables.
Once you have exhausted these, the ~~ operators indicate additional links between factors, or error variances. Be careful here. Most analysts accept adding links between error variances for observed variables that form the same latent variable, or for observed variables that have some relationship not captured by the latent variables in the model (e.g., measurement method, perhaps).
Best Answer
I use OpenMx for SEM modeling where I simply use the omxGraphViz function to return a dotfile. I haven't found it too inflexible -- the default output looks pretty good and though I've rarely needed to modify the dotfile, it's not hard to do.
Update By the way, Graphviz can output SVG files, which can be imported into Inkscape, giving you the best of both worlds. :)